# What is the Sandbox?

This "Sandbox" is a place where Code Golf users can get feedback on prospective challenges they wish to post to the main page. This is useful because writing a clear and fully specified challenge on the first try can be difficult. There is a much better chance of your challenge being well received if you post it in the Sandbox first.

See the Sandbox FAQ for more information on how to use the Sandbox.

## Get the Sandbox Viewer to view the sandbox more easily

To add an inline tag to a proposal use shortcut link syntax with a prefix: [tag:king-of-the-hill]

• How are tags added to questions? – guest271314 Jan 9 at 7:51
• @guest271314 You can use this markup to create a tag in a draft: [tag:code-golf] – DJMcMayhem Aug 29 at 15:19

## Powerful numbers integermath

Look at the number 81 expressed as the sum of distinct powers of the same base:

• 81 = 81 (well, duh)
• 81 = 80 + 1 (easy)
• 81 = 9*9
• 81 = 4*4*4 + 4*4 + 1
• 81 = 3*3*3*3
• 81 = 2*2*2*2*2*2 + 2*2*2*2 + 1 (if you thought that was obvious...)
• 81 = 1 + 1 + ... + 1 (yeah, yeah...)

As you can see, for N > 4, there are always 4 trivial bases: 1, 2, N-1 and N. Powerful numbers are those numbers which have at least one nontrivial base. Please write a program or function that, given a number N > 4, outputs a truthy or falsy value for whether a nontrivial base exists. The results for N up to 30 should be as follows:

(1  F)  16  T
(2  F)  17  T
(3  F)  18  F
(4  F)  19  F
5  F   20  T
6  F   21  T
7  F   22  F
8  F   23  F
9  T   24  F
10  T   25  T
11  F   26  T
12  T   27  T
13  T   28  T
14  F   29  F
15  F   30  T


This is , so the shortest solution wins!

• "Your challenge is, given a number N, to return the Nth Powerful number." I doubt that there's any way to generate the Nth number other than counting up from 1 and stopping once you've encountered N of them. So why not reduce it to "given a number, determine whether it's powerful"? – Martin Ender Jan 19 '17 at 12:13
• Simplified definition: "a powerful number is a number which can be written using only the digits 0 and 1 in any base other than 1, 2, n, or n-1." – user62131 Jan 19 '17 at 15:37
• I believe a (very golfed) reference implementation in ES6 to determine whether a number is powerful would be a=>(g=b=>b>1&&(f=c=>c&&c%b|f(c/b|0),f(a)<2)+g(b-1))(a)>3. This gives these first 1000 powerful numbers. The sequence doesn't seem to be on OEIS though. – ETHproductions Jan 19 '17 at 17:36
• @MartinEnder I was under the impression that it was more common to ask for the Nth or first N terms rather than just verifying a particular term. Perhaps if I ask for all Powerful numbers up to N? – Neil Jan 19 '17 at 21:01
• @Neil I think that's even worse. That way you make 100% sure that there's no way to avoid wrapping the entire program in a boring loop. – Martin Ender Jan 19 '17 at 21:10
• I like challenges like this better as a decision-problem, since that's what it comes down to. Outputting the Nth such number or the first N just adds extra code around the real meat of the challenge. – ETHproductions Jan 19 '17 at 22:03
• Example for first N terms: codegolf.stackexchange.com/questions/107420/… – Neil Jan 20 '17 at 9:45
• @MartinEnder OK, how about if, given an integer N greater than 1, the result should be the number of representations? – Neil Jan 20 '17 at 19:18
• @Neil That's fine, but I'm curious why you're so strongly opposed to making it a simple decision problem. :) – Martin Ender Jan 21 '17 at 14:38
• @MartinEnder You want people to add extra code to compare the result to 4 around the real meat of the challenge? (Sorry I couldn't resist!) – Neil Jan 21 '17 at 15:48
• Quoting me now, are you? :P But you don't actually have to count all of them since 4 are already given: 1, 2, n-1, and n. So all you really have to do in a decision-problem is check if there are any between 3 and n-2, inclusive. – ETHproductions Jan 21 '17 at 22:40
• That said, I'm not sure which path would be shorter in most langs. My attempts in JS for both versions of the problem turned out the same length. – ETHproductions Jan 21 '17 at 23:37
• @ETHproductions OK I'm convinced now. – Neil Jan 22 '17 at 1:08
• Related OEIS sequence – ETHproductions Jan 22 '17 at 22:23
• I actually don't know whether decision-problem would be better than just counting how many bases it's powerful in. There are arguments for and against each. My solutions turned out the same length in JS, but in Jelly the decision-problem solution came out as just 2 extra bytes added to an 8-byte counting solution. I guess it just comes down to what you want to see in the challenge. – ETHproductions Jan 23 '17 at 16:48

# Does Mathematica Have a Builtin?

Your task is to take in a question names and its tags; and to guess whether or not Mathematica has a builtin that solves that question.

## Rules

• Your code must be less than 100 bytes long.

• You may use internet to access the Mathematica reference guide you may also use the internet to access the tag wikis. Standard loopholes apply to internet access.

• For this challenge we will consider a valid builtin to be a builtin that does most of the computation for the challenge. Extra bytes spent on trivialities like IO formatting will be ignored.

• You must output a truthy value if Mathematica has a builtin to solve that challenge and a falsy value otherwise.

• If Mathematica has a builtin and for some reason the challenge does not allow Mathematica to compete or bans builtins your program must still output truthy.

## Scoring

This is a so you will be scored on the percentage questions here (This is currently a work in progress there will be more cases in the final question) that your program gets the correct answer on.

• As always with builtins, you'll want to outline exactly what counts as "built-in". For example, if a challenge is about printing hexagonal numbers, does using PolygonalNumber with fixing r = 6 count? (not sure if that's an accurate example, but you get the point). The test battery would make things 100% indisputable, but it's something you might want to think about when making the test battery. – Sp3000 Jan 26 '17 at 1:55
• On a side note, is a hardcoded approach okay, e.g. regex golfing the pass vs fail set? – Sp3000 Jan 26 '17 at 1:55
• @ETHproductions I meant the later, a function that does most of the work. I am not sure if I am going to write a super strict definition of builtin but I will be writing at least a loose one. – Sriotchilism O'Zaic Jan 26 '17 at 1:57
• @Sp3000 Hardcoded is fine. I would like to see all sorts of approaches to this problem including regex. – Sriotchilism O'Zaic Jan 26 '17 at 1:58
• My question codegolf.stackexchange.com/questions/107181/… was solved in Mathematica with a built-in that I wasn't expecting. That might be useful for your tests – Gareth Jan 26 '17 at 9:22
• Can you read the Mathematica answer off the page if it exists, or is the idea to only read the question? – xnor Jan 26 '17 at 9:40
• @Gareth Thanks I am in need of more test cases. – Sriotchilism O'Zaic Jan 26 '17 at 12:52
• Answer: Hardcode truthy because Mathematica ALWAYS has a builtin :P – user42649 Apr 10 '17 at 13:05

# Minimal QWERTY

The task -- to output the layout of a QWERTY keyboard:

QWERTYUIOP
ASDFGHJKL
ZXCVBNM


But, you will be scored based on the length of your code, and on the number of distinct characters in it.

# Rules

1) The code must output the three lines of text above (or the text above with optional trailing newline)

2) Standard loophole restrictions apply

3) If the language contains predefined information about the QWERTY layout, you are not allowed to use that information.

# Scoring

The score will be defined as [Length of the program in bytes]*[# of distinct characters in the program], with lowest score winning.

For example, the code

ABAB1212


would have score 8*4=32 since it has length 8, but only 4 distinct characters: AB12

And the code:

ABC!!!{{{


Would have score 9*5=45, since it has length 9, and 5 distinct characters: ABC!{

• I really like this scoring system; it strikes a great balance between cutting down chars and cutting down the number of distinct chars you're using. I was going to say that this might not be the best way to use this scoring system, but anything other than "output this exact string" would likely be solvable in 10 bytes in golfing languages, or not solvable in 100 in non-golfing langs. (Perhaps a string with more repetition would work better though, but we won't know until the challenge is posted.) – ETHproductions May 6 '17 at 20:31
• About "If the language contains predefined information about the QWERTY layout, you are not allowed to use it.": does this mean you're not allowed to use the language, or just the QWERTY built-in? – ETHproductions May 6 '17 at 20:33
• @ETHproductions Thanks for the input! The reason I thought thought the QWERTY task would work well with this scoring system is that the output consists almost entirely of a large number of distinct characters (meaning any substantial use of string literals for the output would be very bad for the score), and those characters are fairly disordered, meaning a simple loop won't solve it. Do you have thoughts on other possible tasks for this scoring system? – Maria May 7 '17 at 1:54
• Regarding your second question -- the language would be allowed; they just wouldn't be allowed to use the predefined information. I've changed the wording to make that clear (I see that it was ambiguous before - thanks for catching that) – Maria May 7 '17 at 1:58
• May be too close to this challenge. It's not quite the same, but the basic task is similar (golf down a large set of distinct characters into a set of mostly repeated characters). This challenge is even closer, requesting printing a constant string with many distinct characters, and using the same scoring method; that's almost certainly a duplicate at this point. – user62131 May 7 '17 at 2:23
• @ComradeSparklePony I think this is covered by the condition to exclude this? – Paŭlo Ebermann May 7 '17 at 21:02
• @PaŭloEbermann Oops, I missed that. – Comrade SparklePony May 7 '17 at 21:05
• +1, when are you going to post this? – MD XF May 10 '17 at 1:22
• I kinda agree with @ETHproductions first comment regarding a string with more repetition and non-golfing languages. For example, to solve this in fewest bytes in Java 7 (I know, Java 7 is verbose as F.. xD), it will be: String r(){return"QWERTYUIOP\nASDFGHJKL\nZXCVBNM";} (score of 51 bytes * 41 unique characters = 2091). With fewest characters possible you'll abuse unicodes and it becomes pastebin.com/unrn6xj2 (too long for comment..), with a score of 343 bytes * 18 unique characters = 6174.. But of course, you're free to post it nonetheless as is. Java won't ever compete anyway ;) – Kevin Cruijssen May 10 '17 at 9:07
• But I like the scoring mechanism, and it's also a fairly easy challenge for most golfing languages, where the size vs unique characters really matters, which is of course the focus of code-golfing languages. So perhaps just post it, and I'll just score 2091 with my Java 7 answer. ;) – Kevin Cruijssen May 10 '17 at 9:10
• Japt, 4 points ;D :D – caird coinheringaahing May 19 '17 at 20:13

This message is open for anyone to adopt and post to main. For more details, see the chat room or meta post.

# Nonogram it

Nonograms are one of my favorite types of puzzles, but sometimes there are not enough of them to solve!

The challenge here is to write a program that would take an image and output the values for the columns and rows of the puzzle.

INPUT: black and white PNG on STDIN

OUTPUT: two lines with the values to create the puzzle. First line is the columns, second the rows. The format of both lines is: [a,b,c...],[d,...],... (lists of integers separated with commas delimited with [], with each list separated by commas, ending in a newline. No dangling commas allowed inside the lists or at line end)

The squares on the image should be of 5x5px. The thereshold for determining if a square is filled is if it has at least 30% black inside it.

(3 sample images will be added later)

I'm not sure about the scoring for this challenge, most likely it should be a .

Additional scoring criteria I can think of:

• allowing to enter square size or cols*rows of the puzzle.
• accepting non black and white images
• providing a solver
• wait, is the PNG itself in the STDIN, or a file path to it? I assume the latter, but it's currently formulated as if it's the former. Also, the threshold needs to be clarified. Also, why is the image scaled up in the first place? – John Dvorak Mar 26 '14 at 19:59
• Also, I'd prefer an ascii-art input (a grid of hashes and spaces) than having the challenge complicated by looking up and interfacing an image manipulation API. – John Dvorak Mar 26 '14 at 20:02
• It could be a file path if that's more accesible. I didn't say the image was scaled, the 5*5 squares are for the grid to create the nonogram, just to avoid another required parameter(number of cols*rows desired). About the ascii-art, that would have no challenge, just a count() – Einacio Mar 27 '14 at 15:42
• I don't think a PNG library showoff is a good challenge for this site. There's no thinking present, just having to learn an API and hope it has short enough names. – John Dvorak Mar 27 '14 at 15:45
• I don't understand the 5x5 rule. Is it that there are 5x5 pixels in the image, and 5x5 pixels in the grid? 5x5s are no puzzles. – John Dvorak Mar 27 '14 at 15:46
• It wouldn't be the first challenge using PNG, so I see no problem there. About the grid, I'll prepare the example images later, I hope that'll be clearer to understand – Einacio Mar 27 '14 at 16:02
• Seeing that you prescribe exactly how black and white cells are to be determined, unique solubility of the resulting nonogram is no criterion? – Martin Ender Mar 31 '14 at 11:28
• @m.buettner I proposed the fixed grid and cell criterion with the idea of being able to check results against others. I forgot about ambiguous solutions, and I don't know how difficult is to test for it, specially if it ends as a code-golf. Maybe I should rule it out explicitly to keep answers simpler? – Einacio Mar 31 '14 at 14:18
• @Einacio well, uniqueness could be checked with a solver (there might be easier ways). I suppose you just have to decide whether you want soluble or comparable answers. If you are going for soluble, you can make this a "code challenge" and determine the score based on both code length and similarity to input image. – Martin Ender Mar 31 '14 at 14:58
• Hello! This looks like a good but abandoned meta post, would you be willing to offer it for adoption? (If you want to, you can still post to main.) Due to community guidelines, if you don't respond to this comment in 7 days I have permission to adopt this. – programmer5000 Jun 9 '17 at 16:29
• @programmer5000 Hi, I totally forgot about this challenge, I haven't had much free time in those 3 years to give it some love. I would be delighted to see someone pull it through, do I have to do something more than post it in the chat? – Einacio Jun 9 '17 at 19:40
• @Einacio just post a link to this answer and nothing else in that chat room. – programmer5000 Jun 9 '17 at 19:55

You are a robber in the ASCII world. ASCII lock-key work in similar fashion as the real-world: matching ridges. Your objective is to write a program which generates a duplicate key for the ASCII locks.

Example:

A Lock is given as:

   |\    |\
__| \___| \____
|               |
|_______________|


Its key shall be something like:

 _______________
|   __     __   |
|  |  \   |  \  |
|__|   \__|   \_|


The fit being something like:

 _______________
|   __     __   |
|  ||\\   ||\\  |
|__|| \\__|| \\_|
|               |
|_______________|


# SandBox

I think the fit is weird. It didn't go as I had imagined when I finished typing in the ASCII drawing.

• This has potential, but it needs a clear specification as to what a fit is, and what constitutes a lock (i.e. some constraint on the input). – VisualMelon Jun 14 '17 at 17:47
• Yes. This is very incomplete/unclear as of yet. – officialaimm Jun 15 '17 at 3:27

# Sandbox

This will be my first kolmogorov-complexity submission, does this question fall under that category?

Is the question clear enough?

Is it too trivial?

# Problem

Given no input write a program or a function that outputs or returns the following string:

(<(<>(<>.(<>.<(<>.<>(<>.<>)<>.<>)>.<>).<>)<>)>)

# Rules

• Shortest program wins.
• Trailing whitespace allowed.
• Trailing newlines allowed.
• Unused parameters for functions allowed.
• Can you give more context to the string you're outputting, its significance etc? – Pureferret Jun 15 '17 at 11:24
• It's a poor ASCII representation of a crowd of blank stares a single person being (<>.<>) – LiefdeWen Jun 15 '17 at 11:25
• a more common representation being (-_(-_(-_(-_(-_-)_-)_-)_-)_-) – Skidsdev Jun 15 '17 at 11:28
• @Mayube Yes, I just used a broader face so the outputted string is longer – LiefdeWen Jun 15 '17 at 11:29

## When did I need to be born to celebrate a magic birthday?

I was born in 1984 and in 2016 I became 32 years old, which is 20 in base 16, what a coincidence!

Your task is, given the year of interest -say 2016- , to calculate the year I had to be born to be able to say In 2016 I have celebrated/I will celebrate my 20th birthday (in base 16).

1. take n-digit decimal number - the year xy.
2. Split it in half, if n is odd, the digit the middle is appended to number side.
3. Calculate the year I had to be born to be x base ys old in the year of xy.

Your code shall return Not-a-Number or error message if the decomposition cannot be resolved.

Walkthough:

>  foo(2016)
1: '2016' -> '20' '16'
2: 20 base 16 = 32
3: 2016-32 = 1984
>> 1984

> foo(445)
1: '445' ->'44' '5'
2: 44 base 5 = 24
3: 445-24 = 421
>> 421

>foo(7)
1: '7' -> '7' ''
Error, base not defined
>> nan

>foo(10)
1: '10' -> '1' '0'
Error, base 0 don't exist
>> nan

>foo(1805)
1: '1805'->'18' '5'
Syntax error
>> nan


Test cases:

 7    : nan/error
10    : nan/error
78    : 71
445   : 421
1024  : 1000
1805  : nan/error
1936  : 1891
1984  : 1891
1999  : 1891
2016  : 1984
2015  : 1985
10002 : 9998
10912 : 10759
116015: 115769


Shortest answer in bytes wins. Standard loopholes apply.

• Boo-urns to input validation! Can you add a full example? – Shaggy Jun 21 '17 at 16:14
• Do you mean full ungolfed code or full path from, say 445 to 421? – Crowley Jun 21 '17 at 16:25
• Just a walkthrough of how to get from input to output. – Shaggy Jun 21 '17 at 16:26
• @Shaggy Thanks for sugegstion. Is it better now? – Crowley Jun 21 '17 at 17:16
• Shouldn't 1999 result in 1891? – Emigna Jun 22 '17 at 8:49
• @Emigna Correct. Updated. – Crowley Jun 22 '17 at 13:36

# Don't step on a crack, or you'll break your mother's back

Earlier I was walking down the sidewalk in my town, which is made of concrete slabs and looks something like this (note: not my sidewalk). I decided to try to pace myself such that I didn't step on the little cracks between the concrete slabs. For simplicity, let's say:

• Each slab is 4 feet long.
• Each of my feet is 1 foot long.
• Each crack has 0 width (just like your neighbors' dog).

My natural stride is about 3 feet, which worked out quite well:

(Excuse my horrible MS Paint skills)

Then I got a little ambitious and decided to take 4-foot strides. This obviously worked out even more nicely (aside from making my legs feel weird):

This got me thinking, what other lengths of strides could I take? One non-integer example would be 2⅔ feet:

I could go as short as 1-foot strides, though anything shorter than 1 foot would place my foot-long foot on every crack in the sidewalk. (I didn't do 1-foot strides because I would look weird shuffling down the sidewalk, and also because I was in a rush.)

In fact, there are 6 possible crack-avoiding strides up to four feet: 1, 1⅓, 2, 2⅔, 3, 4.

# Challenge

Given a integer concrete slab length 0 < n < 100, output all stride lengths up to n that I could take on that theoretical sidewalk. Assume I can stretch my legs infinitely far (I am a mathematician, after all).

More mathematically, given an input integer 0 < n < 100, output all numbers 0 < k <= n such that no multiple of k, modulated by n, is greater than n - 1.

Expected outputs for inputs 1 through 9 (rounded to 4 decimal places):

1: [1]
2: [1, 2]
3: [1, 1.5, 2, 3]
4: [1, 1.3333, 2, 2.6667, 3, 4]
5: [1, 1.25, 1.6667, 2, 2.5, 3, 3.3333, 3.75, 4, 5]
6: [1, 1.2, 1.5, 2, 2.4, 3, 3.6, 4, 4.5, 4.8, 5, 6]
7: [1, 1.1667, 1.4, 1.75, 2, 2.3333, 2.8, 3, 3.5, 4, 4.2, 4.6667, 5, 5.25, 5.6, 5.8333, 6, 7]
8: [1, 1.1429, 1.3333, 1.6, 2, 2.2857, 2.6667, 3, 3.2, 3.4286, 4, 4.5714, 4.8, 5, 5.3333, 5.7143, 6, 6.4, 6.6667, 6.8571, 7, 8]
9: [1, 1.125, 1.2857, 1.5, 1.8, 2, 2.25, 2.5714, 3, 3.375, 3.6, 3.8571, 4, 4.5, 5, 5.1429, 5.4, 5.625, 6, 6.4286, 6.75, 7, 7.2, 7.5, 7.7143, 7.875, 8, 9]


The expected output for 99 can be found in this Gist. The length of each output corresponds to A002088.

## Rules

• The input will be a positive integer less than 100.
• The output may be presented in any reasonable format. Entries can be represented as decimal numbers accurate to at least 3 decimal places, or as exact fractions if desired.
• The output may be unsorted, but it may not contain duplicates.

This is , so the shortest code in bytes in each language wins.

• It took me a bit to identify that a foot is 1 foot long. I'd make that more clear. – Nathan Merrill Jul 7 '17 at 17:52
• @NathanMerrill For a second I thought that you were joking :P Should be more clear now. – ETHproductions Jul 7 '17 at 18:33
• output should always be less or equal to input. am i underestood correctly – tsh Jul 7 '17 at 23:46
• @tsh Right, I've clarified that a little more. – ETHproductions Jul 7 '17 at 23:52

# TL;DR:

Given a set of strings, determine whether the characters expose a total ordering based on location in the strings.

In this challenge, strings are used as a predicate to determine the order in which characters should appear in this set. For example, the string

"ONE"

Says:

• All instances of "N" should appear only after instances of "O"

• All instances of "E" should appear only after instances of "N"

By this reasoning, the string "FOOOONZAi.EE" follows this ordering, but "NEEEE3#?EAO" does not (there is an "O" after an "N").

Your challenge is to take a set of strings and determine whether these strings define a total ordering without any logical flaws. This would occur as a cycle of any length, such as:

...or such as:

etc.

Rather than strings, you may take in lists of characters or integers if you wish.

Since this is a , you may output any two consistent values for yes or no, such as true and false, zero and non-zero, exception and no exception, etc. Just specify your output format in your answer.

# Test Cases

["ONE", "TWO", "THREE", "FOUR", "FIVE", "SIX"] -> true (one possible ordering is "TWFOUIVXNHRE")
["ZERO", "FOUR"] -> false ("R" must follow "O", but "O" must follow "U" which must follow "R")
["", ".", "forty", "this->~why();", " -y."] -> true
["AB", "BC", "CD", "DE", "AC", "BD", "CE", "EA"] -> false

(more can be written if needed)


# Scoring

This is , so the shortest answer in each language wins.

# Sandbox

How can I make this more clear? Any suggestions?

• This could be more general if you allow lists as input rather than strings. – lirtosiast Jul 13 '17 at 22:18
• @lirtosiast So a list of lists of characters? – musicman523 Jul 14 '17 at 0:52
• I would recommend lists of integers instead of strings. I feel the challenge would be "cleaner" that way, but that's up to you. Also, you should have a test case where where each pair is consistent but the whole set isn't. – Zgarb Jul 15 '17 at 7:17
• Is this not effectively the same as your previous challenge of whether a directed graph has a cycle? – xnor Jul 16 '17 at 1:19
• @xnor I suppose it is, though I think the challenging part is collecting the edges by vertex. How about this: I rewrite the challenge to be "Give a valid ordering for a set of strings, guaranteed that one exists"? – musicman523 Jul 16 '17 at 3:49
• @musicman523 I remember a DAG sorting challenge, I think that would be a dupe of it. – xnor Jul 16 '17 at 3:52

# Self-Improvement

You must create a self-mutable program that, when run, outputs a non-zero integer and also overwrites the file with a program that outputs double the number.

For example, if I run the program self-improvement and it outputs 10, it must output 20 when I run it the second time, output 40 the next time, and so on.

• You must not rely on any file on the computer other than your program.
• Said program must consist of only one file.
• Of course, no loopholes that are banned from the entire site.
• You can assume that your program won't go tested beyond the range -2^16 to 2^16-1.
• no loopholes banned -> no loopholes that are banned, overwrite -> overwrites. Also, something on how far this needs to go might be important - does it have to work infinitely, or only to INT_MAX for the language in question? If you choose the second option, keep in mind language with very small numeric caps. Otherwise, welcome to PPCG, I really like this question, and I'm glad you Sandbox'd it :) – Stephen Jul 17 '17 at 21:33
• @StepHen Thanks; I decided that they can assume that the parameters won't go beyond INT_MAX. – Lawful Lazy Jul 17 '17 at 21:38
• In case anyone needs to find it at some point, don't forget about this standard loophole. – Stephen Jul 17 '17 at 22:24
• @Artyer I stated "any nonzero integer". That excludes 0. – Lawful Lazy Jul 17 '17 at 22:55
• @LawfulLazy I didn't read that too well. – Artyer Jul 17 '17 at 22:58
• @Artyer I'll make sure to embolden it. I've also set a minimum integer range for StepHen. – Lawful Lazy Jul 17 '17 at 22:59

# Deduplicate equivalent expressions

Suppose we wanted to generate all expressions containing at most 2 of + and −. We might have a list like this:

a + b + c         b + c + a
a + b - c         b + c - a
a - b + c         b - c + a
a - b - c         b - c - a
a + c + b         c + a + b
a + c - b         c + a - b
a - c + b         c - a + b
a - c - b         c - a - b
b + a + c         c + b + a
b + a - c         c + b - a
b - a + c         c - b + a
b - a - c         c - b - a


There is a lot of repetition here. It surely isn't necessary to include all of a + b + c, a + c + b, b + a + c, b + c + a, c + a + b, and c + b + a, since they all mean the same thing. This can be deduced from knowing that, for any x and y, x + y is the same as y + x.

Similarly, b + a - c and a - c + b are equivalent. To deduce this, one must know that, for any x and y, x - y is the same as x + (-y).

Let's assume the following:

[1]: a + b == b + a
[2]: a - b == a + -b


Then, we can deduce that b + a - c and a - c + b are equivalent:

start:  b + a - c
b + a + -c        by 2
a + b + -c        by 1
a + -c + b        by 1
end:    a - c + b         by 2


Therefore, they are the same. After performing similar proofs, we are left with the list:

a + b + c
a + b - c
a - b + c
a - b - c
b - a + c
b - c - a
c - b - a


## Definition of an expression

An expression can be described as:

variable   = "a" | "b" | "c" | ... | "y" | "z";
digit      = "0" | "1" | "2" | ... | "8" | "9";
number     = digit . digit*;
operator   = "!" | "#" | "$" | "%" | "&" | "*" | "+" | "~" | "-" | "." | "/" | ":" | ";" | "<" | "=" | ">" | "?" | "@" | "^" | "_" | "" | "|"; data = number | variable; subexpr = data | operator* . data; expression = subexpr | subexpr . operator . expression;  Where | suggests alternatives, . suggests concatenation (with potential whitespace around each operand), * suggests "0 or more times", and " is a string literal. x + y, j * i - 3, u & 4 * 2 < ~4, q % ~*^t and r are all expressions. You should assume all operators are left-associative. ## Definition of assumptions An assumption is a pair of expressions said to be equivalent. This means one can be transformed into the other. When performing a transformation using an assumption, one replaces all the appropriate variables and maintains the numbers as they are. (These "variables" can also be sub-expressions, which is any expression not using an operator in the assumption.) For example, if the assumption is !a == a + 5, then one can transform t + 5 into !t and 3 + 5 into !3. Another example: if the assumption is a + b == a * b @ b, then 5 + 2 can become 5 * 2 @ 2 and z * 3 @ 3 can become z + 3, but z * 4 @ a cannot be reduced further using this rule. One last example: if the assumption is a < b == a, then 1 + 3 & 5 < 2 * 3 + 6 would become 1 + 3 & 5, and 1 + 2 < x + y < 7$ q would become 1 + 2, since it would be equivalent to (1 + 2) < (x + y) < (7 \$ q), which is thus 1 + 2.

If either side of the assumption is a single variable, numbers are excluded from this assumption. E.g., the assumption a == 3 would only apply to variables.

## Expression equality

Two expressions are equal if they can be proven to be the same. Variables must be the same for each expression; for example, a + b is not by default the same as b + c.

## Challenge

Your task is to remove "duplicate" expressions given some assumptions. You can use any unambiguous symbol or method, including taking a pair of strings, to represent an expression. The expressions remaining in the result do not necessarily have to be in the set, but must be equivalent by the given assumptions. E.g., if you have a + b - c and b - c + a in the input, you can have -c + b + a represent these in the resultant set. You should try each equation in the order that it's given to you (to simulate "precedence").

The input consists of a list of assumptions and a list of input expressions. The input expressions can be an array or container of strings or string pointers, or in any way standard to your language. (E.g., for C, one should expect null-terminated strings.) The input format must be consistent for all runs.

The output can be a list representation (as is standard to your language), can be separated by newlines (\r, \n, and \r\n are acceptable), or separated by commas. The output format must be consistent between runs.

This is a , so the shortest program in bytes wins.

## Test cases

Every output is merely an example, and is not the only valid output.

Assumptions: { e1 == e2, e3 == e4, ... eN-1 == eN }
Input: { expr1, expr2, ... exprN }
Output: { expr1, expr2, ..., exprK }

Assumptions: { "a + b" == "b + a" }
Input: { "3 + 4", "4 + 3", "5 * a", "a + 2", "2 * a", "a * 5", "a + b", "2 + a" }
Output: { "3 + 4", "5 * a", "a + 2", "2 * a", "a * 5", "a + b" }

Assumptions: { "a + 0" == "a", "a * 1" == "a", "a * b" == "b * a", "a + b" == "b + a" }
Input: { "1 * 2 * 3", "3 * 2 + 0", "1 + 2 + 3" }
Output: { "1 * 2 * 3", "1 + 2 + 3" }
OR: { "2 * 3", "1 + 2 + 3" }

Assumptions: { "~a" == "a ~ a" }
Input: { "~z", "z ~ z", "~a", "~~a", "a ~ a ~ a ~ a" }
Output: { "~a", "~z", "~~a" }

Assumptions: { "a + b" == "0" }
Input: { "x + y", "0", "3 + y + a + v + k", "75", "4 + 2" }
Output: { "0", "75" }

Assumptions: { }
Input: { "x + y", "x + y", "y + x", "3", "3 ! 3" }
Output: { "x + y", "y + x", "3", "3 ! 3" }

Assumptions: { "j" == "3" }
Input: { "v + t", "z", "q", "q + r + t", "4 + 2" }
Output: { "v + t", "z", "q + r + t", "4 + 2" }

Assumptions: { "a" == "b" }
Input: { "a", "b + c", "e % t", "q & t", "!3", "z" }
Output: { "a", "b + c", "e % t", "q & t", "!3" }

Assumptions: { "1 & 0" == "0", "1 & 1" == "1", "0 & 0" == "0", "a & b" == "b & a", "0 ? a : b" == "b", "1 ? a : b" == "a" }
Input: { "1 & 1 & 0", "j & k", "y & z", "z & y", "1 & 0 ? k & j : 0" }
Output: { "0", "j & k", "y & z" }

• Several of your expressions are inconsistently quoted. I also think you should explain what should happen when the assumption is something like 3 == a. Would I remove one of: 5, 7? It seems if you had a == b as the assumption you would, but the other one is counter-intuitive to me. Also, a == b is rather odd on its own, perhaps that is also a good test case. Also, the empty assumption if you intend to allow it. – FryAmTheEggman Jul 17 '17 at 3:18
• @FryAmTheEggman Could you clarify your first question? Are you asking what should happen if 5, 7 is the input given the assumption a == 3? – Conor O'Brien Jul 17 '17 at 4:00
• Yes, that's what I meant. – FryAmTheEggman Jul 17 '17 at 4:08
• 1. subexpr = data | operator* . data; is surely equivalent to just subexpr = operator* . data;? 2. For the second test case it would be more illustrative to include an example output like { "0 * 2 + 3", "1 + 2 + 3" }. 3. I'm not sure what you mean by "If either side of the assumption is a single variable, numbers are excluded from this assumption". Is it that an assumption a == 3 with input {"b == 2", "c == 2", "4 == 2"} should give output e.g. {"3 == 2", "4 == 2"} rather than {"3 == 2"}? – Peter Taylor Jul 17 '17 at 7:43
• @PeterTaylor 1. yeah, I original had * mean "1 or more"; will fix. 2. good idea. 3. Well, the way that input would be parsed is b = = 2, with a binary = followed by a unary =. Could you perhaps use a different symbol? I don't quite understand your confusion. – Conor O'Brien Jul 17 '17 at 16:53
• Sure: assumptions: { "a" == "3" }; input: {"b + 2", "c + 2", "4 + 2"}. Is {"3 + 2", "4 + 2"} the correct output? – Peter Taylor Jul 17 '17 at 18:03
• @PeterTaylor Yes, it is. – Conor O'Brien Jul 17 '17 at 18:34
• The definition of assumptions includes an assumption with more than one operator, but none of the test cases do. I would think that's an important thing to test. – Peter Taylor Jul 26 '17 at 11:06
• @PeterTaylor Added. – Conor O'Brien Jul 26 '17 at 19:32

# Levenshtein distance using only SO titles code-golf

Pick 1 or as many titles as you wish from revisions of questions from Stack Overflow. You now have a tuple of all of the characters used in the titles you picked. You may add up to as many newline characters as titles you picked. Using exactly all the elements (characters) in this tuple (you may chose lower or upper versions of each character) write a program or a code snippet that computes the Levenshtein distance between two strings.

That's it. Happy title hunting!

## Clarifications and rules:

### Revisions

• We define a revision as seen on https://stackoverflow.com/posts/XXX/revisions
• for a question without any revision (not edited after being posted), the question itself counts as a revision
• all revisions are eligible, from the initial posted question to the current version of the question
• the revision must be created before 10PM 21 July GMT (before the time of posting this challenge on the sandbox)
• only questions from Stack Overflow qualify (no meta, no other site)
• deleted questions qualify (the only exception: spam questions don't qualify). I realize not everybody has access to deleted questions, but a question can become deleted after you post so I decided to allow it, especial considering the very large number of non-deleted questions: you have where to pick from.
• you may pick one revision multiple times. You may pick multiple revisions from the same question.

For instance you pick these hypothetical titles from valid revisions:

• To be?
• ...Or not to be? you pick this one 3x
• Pls. help me!!

Then the tuple you have is this (between "):

"            !!..........????bbbbeeeeeehllmnnnoooooooOOOpPrrrsttttttT"


to which you may add up to 5 new line characters.

You must use all of these characters (nothing less, nothing more) to write your code. In this example your code must contain exactly 12 (space) characters, 2 ! characters, 10 . characters, 4 ? characters, 4 b/B characters etc.

Lower/upper case: regardless of the character case in the title, you may use any case you want for each. In this example you can use (4 b) or (3 b and 1 B) or (2 b and 2 B) or (1 b and 3 B) or (4 B). Upper/lower as defined on http://www.fileformat.info - Unicode data table

Here are all the character you must use in this example:

+----+-----+
|    |  12 |
|  ! |   2 |
|  . |  10 |
|  ? |   4 |
|  b |   4 |
|  e |   6 |
|  h |   1 |
|  l |   2 |
|  m |   1 |
|  n |   3 |
|  o |  10 |
|  p |   2 |
|  r |   3 |
|  s |   1 |
|  t |   7 |
| \n | 0-5 |
+----+-----+


### Code

• You may write a program or a function and use any of the standard methods of input/output.
• input must be 2 strings
• you can assume both of the 2 strings are not empty
• you cannot take other input
• output must be a number representing the Levenshtein distance between the two strings as defined on wikipedia. You may output leading and trailing white spaces (including new lines).
• you must not output anything else
• You may use any programming language, but note that these loopholes are forbidden by default

### Score

This is , so the shortest valid answer – measured in bytes – wins.

## Format

In order to make it easy on everybody, please:

• link the revisions you use
• show each title
• show the final tuple of characters

Meta discussion:

• Should I encourage/discourage/ban using titles already picked by someone else?
• This seems easily abused using comments or other non-executing code. – KSmarts Jul 24 '17 at 15:17
• @KSmarts yes, you would use comments and non executing code, but it will count to your score. If you need to pick a 20 chars title just to get a certain symbol and the rest of the characters you don't use (you put them after a comment start) then maybe that is not a good deal, isn't it? – bolov Jul 24 '17 at 15:59

Challenge: Count integers 1 to 10, but slowly on a time delay.

Your challenge is to print the integers 1 to 10 to the screen with each integer separated by a newline, but on a time delay, such that it should take “n” seconds before the integer “n” is printed to the screen. For example, the program will wait 1 second before printing 1 and a newline, and then the program will wait 2 seconds before print 2 and a newline, and then the program will wait 3 seconds before print 3 and a newline.

So the expected standard output to the screen is this:

1
2
3
4
5
6
7
8
9
10


But the program will patiently wait “n” seconds before printing the integer “n” to the screen, so as your program may interpret it as …

waiting 1 second …

1


waiting 2 seconds …

2


waiting 3 seconds …

3


, and so on …

Restrictions:

1) Since some programming languages may not have a sense of system time, you are not allowed to use any modules/libraries/functions which can measure the time of your program within your program. Therefore all programming languages can be used. This restriction puts all the programming languages on an equal level.

2) Restriction 1 makes it such that you are required to write a function which takes about 1 second to process, and then you can rerun that function “n” integer of times before printing the next integer “n” in 1 to 10 to the screen. You can call your function whatever you want or if you can get away without naming the function then you can do that, too. So, your program would see this behind the scenes:

performing function fx 1 time. #which the arbitrary function fx takes about 1 second to process.

1


performing function fx 2 times

2


performing function fx 3 times

3


… and so on

3) Therefore, your program should take about 1 + 2 + 3 + 4 … + 10 = 55 seconds to finish printing all the integers from 1 to 10 to the screen. Since you need to write a function that takes about 1 second to process, acceptable solutions can be off by plus or minus 2 seconds from 55 seconds.

4) You must time your script which counts the integers 1 to 10 on a delay, so you can use any external program to time your script. I recommend using the bash function time, and giving me the “real” time or actual elapsed time of your script in seconds. If you time your script another way, tell me how you did it. Give me three digits after the decimal place for the real time in seconds. Do not round or truncate.

winning condition:

The winning condition is the fastest program in terms of actual elapsed real time in seconds which is closest to 55 seconds. If, for example, one submission is 54.9 seconds and another is 55.1 seconds, the 55.1 second submission wins because 54.9 seconds is too fast. Again, the point of this program is to slowly print integers to the screen.

Again, it should take approximately 55 +/- 2 seconds to print the integers 1 to 10 to the screen.

• I modified my problem in such a way that no programming language should have an advantage. – xyz123 Jul 28 '17 at 6:17
• you are not allowed to use any modules/libraries/functions which can measure the time of your program Does this mean things like Stopwatch, getting the DateTime, Thread.Sleep, etc? – TheLethalCoder Jul 28 '17 at 9:56
• Nice challenge by the way but I'm not sure I like the winning condition. What's wrong with a code-golf? Also if I was you I'd trim some of the fluff down, at the moment there is a lot of text to information. – TheLethalCoder Jul 28 '17 at 10:00
• Will this not also vary dependent on what machine is running it? I really like the idea but I can imagine it being quite hard to test - especially with that winning condition, as I can imagine it coming down to hundredths of seconds, which would doubtlessly vary depending on the computer running it. Really like the idea nonetheless – space junk Jul 28 '17 at 11:01
• I suppose you could do it by only running them on TIO? TIO's time limit is 60 seconds so you'll have ample time, & it should be a bit more uniform in terms of processing time. – space junk Jul 28 '17 at 11:02
• Yes, TheLethalCoder you would not be allowed to do that. After I thought about, I realize that different computers may have different specifications for runtimes, although I suppose the winning condition could be the least number of bytes, but I was thinking about setting the winning condition to the fastest program which is closest to 55 seconds because if somebody wrote a program which had less bytes, but it was 1.9 seconds over 55 seconds, then it might be too slow for a lot of the other programs which had more bytes, but were faster. – xyz123 Jul 28 '17 at 15:08
• Although if I set the winning condition to the least number of bytes, then I believe that I would have to increase the restraint to acceptable programs cannot be off by +/- 1 second from 55 seconds. – xyz123 Jul 28 '17 at 15:09

# Random number from 0 to n

## Challenge

Write a program/function that, given a positive integer n, outputs a uniformly random integer from 0 to n.

### Input

• Input will be a positive (non-zero) integer.
• It will be in your language's number handling capabilities. // reword

### Output

• Output must be a uniformly (pseudo)random integer.
• Every integer in the range [0, n) must have an equal chance of being outputted.
• You may assume that your chosen language's built-in RNG is uniform.
• Must be in 0 to n, in [0, n), ≥ 0 and < n

### Specifications

• Standard I/O rules apply.
• Standard loopholes are forbidden.
• This challenge is not about finding the shortest approach in all languages, rather, it is about finding the shortest approach in each language.
• Your code will be scored in bytes, usually in the encoding UTF-8, unless specified otherwise.
• Built-in functions that perform this task are allowed but including a solution that doesn't rely on a built-in is encouraged.
• Explanations, even for "practical" languages, are encouraged.

## Test cases

Note that this challenge is tagged and hence will have non-deterministic outputs.

Incoming!

# Sandbox

• We seriously don't have this already?!
• Interesting idea, but how will the test cases work? Also I imagine builtins will be the shortest for many languages – Chris_Rands Aug 9 '17 at 8:39
• @Chris_Rands not all challenges need test cases. – TheLethalCoder Aug 9 '17 at 10:27
• Definition of random? We don't have it because it's a bad idea. – feersum Aug 9 '17 at 11:32
• @Chris_Rands They're going to be random test cases. :P And yes, built-ins, but I'm afraid I don't like banning built-ins. – totallyhuman Aug 9 '17 at 12:39
• @feersum Yeah, I have to iterate over that better. Basically, it has to be uniformly pseudo-random. Any suggestions? – totallyhuman Aug 9 '17 at 12:41
• @AdmBorkBork If you do find a dupe, please let me know! I've searched everywhere and asked in chat, but I couldn't find one. – totallyhuman Aug 9 '17 at 12:42
• Extremely closely related – AdmBorkBork Aug 9 '17 at 12:54
• @AdmBorkBork Aha, I didn't find that (probably because it isn't tagged with number :P). It's very close but it has some arbitrary restrictions... Good enough to have a regular one? – totallyhuman Aug 9 '17 at 13:19
• The only way an answer can be valid here and fail the "arbitrary restrictions" there is if it's a trivial call to a built-in, so this question doesn't add anything to the site. – Peter Taylor Aug 9 '17 at 14:12
• Now define pseudorandom. Also, using a hardware random generator is not allowed? – feersum Aug 9 '17 at 14:16
• @feersum I am not sure how much more I can define "random". I have edited in the fact that you can assume that your language's RNG is uniform. Where have I disallowed hardware random generators? – totallyhuman Aug 10 '17 at 2:07
• it has to be uniformly pseudo-random Pseudorandom is not random. – feersum Aug 10 '17 at 12:23
• So now the only definition of "random" we have is that built-ins that are designated as random number generators are considered "random". So the challenge can only be answered by builtins, since there is no other definition provided. – feersum Aug 10 '17 at 12:24
• @totallyhuman What if the language has a built-in RNG which is not a uniform RNG? – isaacg Aug 12 '17 at 13:09

# Modular multiplicative inverse

Your task is to given two integer numbers, a and b calculate the modular multiplicative inverse of a modulo b, if it exists.

The modular inverse of a modulo b is a number c such that ac ≡ 1 (mod b). This number is unique modulo b for any pair of a and b. It exists only if the greatest common divisor of a and b is 1.

## Input and Output

Input is given as either two integers or a list of two integers. Your program should output either a single number, the modular multiplicative inverse that is in the interval 0 < c < b, or a value indicating there is no inverse. The value can be anything, except a number in the range (0,b), and may also be an exception. The value should however be the same for cases in which there is no inverse.

0 < a < b can be assumed

## Rules

• The program should finish at some point, and should solve each test case in less than 60 seconds
• Standard loopholes apply

## Test cases

Test cases below are given in the format, a, b -> output

1, 2 -> 1
3, 6 -> Does not exist
7, 87 -> 25
25, 87 -> 7
2, 91 -> 46
13, 91 -> Does not exist
19, 1212393831 -> 701912218
31, 73714876143 -> 45180085378
3, 73714876143 -> Does not exist


# Scoring

This is code golf, so the shortest code for each language wins.

• I would've thought this would be a duplicate, but it doesn't look like it is. In particular, this challenge is different. – isaacg Aug 20 '17 at 22:21
• Clarification: Can answers throw an error if there is no inverse? Can they loop forever? – isaacg Aug 20 '17 at 22:21
• @isaacg Thought that as well, was really surprised when I could not find any duplicate. – Halvard Hummel Aug 21 '17 at 6:14
• @isaacg Added some clarification to the text. Allowed errors, but the answers should stop at some point. Also made them have to solve each test case in 60 seconds, as otherwise the challenge would become a bit easy (basically looping over all the possible values) – Halvard Hummel Aug 21 '17 at 6:16

# n-gon in m-gon

What is the greatest equilateral triangle you can fit into a regular pentagon? This is what this challenge is about, but with regular n-gons/m-gons.

### Challenge

Given two integers m,n greater or equal to 3, find the maximal ratio of the areas of the two polygons such that the m-gon is completely contained in the n-gon.

### Details

We are always talking about regular polygons, this means that all sides have the same length and all vertices are on a circle. The output can be a floating point-, fixed point- or rational number and must be correct to three decimal places.

### Examples

 m  n  ratio (area m-gon / area n-gon)
x  x  1 (for all x)
3  4  1/4*sqrt(3) = 0.4330
4  3  12/(7*sqrt(3)+12) = 0.4974
3  6  1/2 = 0.5
6  3  2/3 = 0.6667


Would be nice to have larger examples.

• You may consider changing the language of the initial problem specification and input/output chart to specify that you are comparing the areas of the m- and n- gons – Taylor Scott Sep 26 '17 at 21:37
• I see what you mean but right now I have difficulty coming up with a better wording (english is not my native language), if you have a better suggestion feel free to directly edit it! – flawr Sep 26 '17 at 22:39

I bet I can write down your PIN! 0000 0001 0002 0003 ... 9999.

## Task: Write a program that outputs a string containing all possible four digit PINs.

The string should not contain any whitespace (trailing newline is okay).

## Explanation

The output string only needs to contain each PIN somewhere in it; digits can be reused. For instance the string “123456789” contains the PINs 1234, 2345,3456,4567,5678,and 6789. By reusing digits, it's possible to save a significant amount of space from the naive implementation (0000000100020003...9999).

At best, this could be written as a 10,003 digit string. 4 digit for the first PIN, then one more digit for the other 9999 PINs.

I've written a basic Python script that can check your solution and indicate any PINs you are missing.

import sys
passes = True
for ix in range(10000):
pin = "%04d" % (ix)
if s.find(pin) == -1:
print("Missing PIN %s" % pin)
passes = False

if passes:
print('Result passes!')
print('String length is %d characters.' % len(s))

• Nice, but I think you need to replace code-golf with code-challenge as this isn't just scored by shortest code. – Adám Sep 28 '17 at 22:25
• Very related – H.PWiz Sep 28 '17 at 22:29
• This is just codegolf.stackexchange.com/q/42728/194 with hard-coded input, and hence qualifies as a dupe. – Peter Taylor Sep 29 '17 at 11:08
• Too bad it's a duplicate... but now I know about De Bruijn sequences! – Dominic A. Sep 29 '17 at 23:19
• @PeterTaylor: I think there's one even more dupey than that; I've been trying to find it all day. The "background" to it was a keypad on a building door that had a 4-digit code. – Shaggy Sep 30 '17 at 0:59

## Roll identical boson dice code-golfrandom

When you roll two dice, the chance of a 5 and 6 in either order is a 2 in 36 (or 1/18), since it could happen as (5,6) or (6,5). But (6,6) can only happen one way and has a 1 in 36 chance.

Our dice will instead work as identical bosons: (5,6) and (6,5) are a single outcome {5,6} that is equally likely to {6,6}. So, each of these 21 unordered pairs is equally likely, with chance 1/21.

{1,1}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,2}, {2,3}, {2,4}, {2,5}, {2,6}, {3,3}, {3,4}, {3,5}, {3,6}, {4,4}, {4,5}, {4,6}, {5,5}, {5,6}, {6,6}


Similarly, for 3 dice, [5,5,6], [5,6,5], and [6,5,5] all count as a single outcome {5,5,6}, but [6,5,6] is different.

Task: Output a random roll of n boson dice, so that each possible result is equally likely as an unordered multiset, i.e. when sorted.

It's OK if your output is ordered as long as the overall probabilities are right. You may sometimes output [5,6] and sometimes [6,5] as long as their total chance is 1/21. They don't have to each be 1/42 chance. You could output [5,6] with 1/21 chance and never [6,5].

Input: A positive integer n

Output: A random list of n numbers from 1 to 6, so that each outcome is equally like when taken as an unordered multiset.

Time restriction: Your code has work up to n=50 within 1 minute.

• I think it's unlikely that there'll be an algorithm for this terser than simply constructing the list of all possibilities, then selecting a random element from it. As such, I'm not sure the randomness adds to the task here. It's possible I'm wrong. (I toyed with some methods of restricting complexity to ban this solution, but I couldn't find one I was satisfied with.) – user62131 Jun 22 '17 at 22:48
• @ais523 I know some fairly nice methods to generate these directly, but I don't know if they'll beat out the boring one you suggest. Rolling repeatedly until sorted is also boring and direct. Maybe a complexity restriction is needed. I'll see what I can golf up. – xnor Jun 23 '17 at 7:24
• with the (new) time restriction this is more like math-golf than code-golf. Can you give away any of your "nice methods"? Is it the weighted probability of every digit of the 50-digit number ,one of them? – user72269 Oct 2 '17 at 17:29

## Limited-Information Maze-Solving Bot

(Still in draft/beta format. Feedback welcome.)

Based on a challenge idea I posted in chat and the ensuing conversation. Thanks to NathanMerrill, zgarb, and Jonathan Frech for assistance in fleshing this out.

### The challenge

You're writing two separate programs/functions/routines/etc. The first, which we'll call the helper program, takes the input maze and calls the second, which we'll call the solving bot. The solving bot must solve the maze based on its interaction with the helper program.

The maze is 51x51 characters in size. For clarity in this challenge description, it is composed of # walls and   corridors, but you can use any two distinct, consistent ASCII characters of your choice. E.g., use ! for walls and x for corridors, use 1 for walls and 0 for corridors, etc. This maze is one of many that will be the input to your helper program/function.

The maze start is always guaranteed to be somewhere on the left-most column, and the exit is always guaranteed to be somewhere on the right-most column. The maze is guaranteed to have at least one path from the start to the exit. As a result of this construction, the very top row and very bottom row are all #, and the very left and right columns are all # except for the start and exit.

The solving bot that you're creating needs to find a solution to the maze (not necessarily the shortest), but is limited in that it can only "see" a new 5x5 section of the maze at a time. The bot is scored by how many times it needs to request a new 5x5 section from the helper program/function.

The upper bound is obviously to simply request every possible 5x5 section, for a score of around 100. The lower bound is where someone with perfect knowledge of the maze can request only those 5x5 sections containing the exact route of the shortest solution, possibly as low as 10. Your bot will be run through (1000?) different mazes, and the bot with the fewest total requests will be the winner.

The solving bot is placed on the left-hand side where the start is, and the first 5x5 section is provided for free. However, the bot doesn't know where, vertically, it is on the left-hand side of the maze. It could be in the top corner (as in the example below), in the bottom corner, or anywhere in between.

### Input/Output

The code you're writing be required to take the maze as an input (STDIN, a file to read, etc.) and call a subroutine of some sort for the solution bot.

Input: (1000?) 51x51 mazes Output: How many total requests your solving bot took

Yes, this is a non-observable requirement to be on the honor system and ensure the two "halves" of your program (i.e., the I/O half and the solving half) talk to each other correctly and accurately. I trust the community enough to believe that this is OK.

### Further rules

Your solving bot should be deterministic. That is, when presented with the same maze two or more times, it should request the same number of 5x5 sections.

### Example Maze

(generated from http://www.delorie.com/game-room/mazes/genmaze.cgi )

###################################################
#     # #   # #   #   #         #   # #
# ######### ##### # # # # # # # # # ####### ### # #
#   #       #   #   # # #   # # #         #   # # #
### # ####### # # ### # ### # # ############# # # #
#   #   #   # # #   # #     # #   #   #   # #   # #
# ####### # ### ### ####### # ### # # # # # # ### #
#     #   #       #       # # #   # # # # # # #   #
##### # ################# # # # ### ### # # # # ###
#   #       #     #         # #         # # # #   #
### ####### ##### # ######### ##### ##### # ##### #
#   #           #   #       #     # #   # #   #   #
# ##### ### ### # ### ########### # # # # # # ### #
#       # # #   # # #   #         # # # #   # #   #
######### # ### # # ### # ######### # ##### # # ###
#       # #   #   # # #   #       # # #     # # # #
# ##### # ### ##### # ##### ##### # # # ##### # # #
#     #   #       # # #   #     # #   # #     # # #
### # ####### # ### # # # ##### # ### # ####### # #
#   #     #   #   # #   #   #   #   # # #         #
# ####### # ##### # ####### # ### # ### # ### # ###
# #     # #     # #       # # #   #   #   #   #   #
# # ### # ##### # # ####### # # ##### ####### ### #
#   #   #       # #     #   # #     #   #   # # # #
##### ########### ##### # ########### # # # # # # #
# #   #       #   #   # #       #   # # # # #   # #
# # ### # ##### ### # # ### ### # # # ### # ##### #
#   # # #       #   #     # # #   # #   # #   #   #
##### # # ##### # ##### # # # ##### ### # ### # ###
#   # # #     # #   #   # #   #         #   # #   #
# # # # ##### # ### # ### ##### ### ##### # # ### #
# # #   #     #     # # #         #       # # #   #
# ####### ########### # ############### ##### # ###
#     #   #   #       #             # #   #   # # #
##### # ### # # ####### ######### # # ### # ### # #
#   #     # # # #       #       # #   #   # #   # #
# ##### # ### # # ######### ### ##### # ### # ### #
# #     #   #   #     #   # #   #     # #   #     #
# # ####### ######### # # # ##### ### # # ##### ###
# # # #     #     #   # # #     # # #   #     #   #
# # # # ######### # ##### ##### # # ##### ### # # #
#   #   # #     # # #     #   #     #   # #   # # #
### ##### # ### # # # ### # # ####### ### ### # # #
# #     # # #   # # # #   # #       #       #   # #
# ##### # # # ### # # ##### ####### ####### ##### #
#       #   # #   # #       # #   # #       #   # #
### ######### # # # ######### # # # # ####### # # #
#   #   #   # # # #   #         #   #     #   #   #
# ### # # # # # ##### # ####### ########### ##### #
#     #   #   #       #       #             #
###################################################


Example starting block:

#####

# ###
#   #
### #

• Does the solving bot also have to find the maze's start by scanning the left side or is it placed at the start position? – Jonathan Frech Sep 17 '17 at 19:18
• related – Liam Sep 17 '17 at 21:47
• @JonathanFrech Good point. We'll say that it's placed at the start position and the first 5x5 area is free. – AdmBorkBork Sep 18 '17 at 16:39
• You could maybe only use one space wide corridors, as the second space does not add any information and thus you do not really get a true 5x5 section of the maze. Just a thought, though. – Jonathan Frech Sep 25 '17 at 11:50
• @JonathanFrech No, that's a good point. I went with double-wide corridors since it looks more even with the character height, but looks aren't important when doing this challenge. I'll update the sizing. – AdmBorkBork Sep 25 '17 at 15:54
• Are this maze's dimensions not 51x51? – Jonathan Frech Sep 25 '17 at 16:29
• @JonathanFrech Apparently, with that generator, a size 50 doesn't yield a size 50. I'll either find a different generator or make my own for the actual challenge. Thanks! – AdmBorkBork Sep 25 '17 at 17:28
• I think the problem does not lie in the generator; it lies in the maze's nature. If your corridors are always one character wide and you have walls on the far left and far right, your maze size has to be odd. – Jonathan Frech Sep 25 '17 at 19:13
• Does this allow for "relative" vision? As in, after we get the initial block we would request "The next block to the right" instead of "the block at (2,7)"? – Kamil Drakari Sep 26 '17 at 20:22
• @KamilDrakari Sure, that would be allowed. It's dependent upon how that half of your submission works. – AdmBorkBork Sep 26 '17 at 20:32
• @JonathanFrech Good point. Maybe I'll compromise and make it a 51x51 maze. Thanks for the insight. – AdmBorkBork Sep 26 '17 at 20:32

## Type the alphabet as fast as you can

Your task is to make a program that measures how fast you can type the letters of the English alphabet.

• The program shall only accept lowercase letters a to z in alphabetical order.
• Each letter is echoed as typed on the same line (without new line or any other separators between letters).
• If you type an invalid character the program shall output Fail and exit.
• If you type all 26 letters the program shall output the time in milliseconds it took from the first to the last letter and exit.
• The timer starts when you type the first letter, a.

Example outputs:

b
Fail

abcdefgg
Fail

abcdefghijklmnopqrstuvwxyz
6440


This is , so shortest answer in bytes wins.

• Related. I would also recommend to put "time" in some way into the title. – Laikoni Oct 27 '17 at 13:49
• Thanks @Laikoni – Danko Durbić Oct 27 '17 at 14:53
• Does the output have to be strictly in milliseconds, or at least in milliseconds, e.g. nanoseconds. Many builtin timing functions are in ns these days. – nimi Oct 27 '17 at 16:39

# Stable modular exponents

It is well-known that the final three digits of Graham's number are 387. This is because Graham's number is a ridiculously tall exponent tower of threes: 3^(3^(3^...))), and it can be shown that any such tower of height at least 5 has 387 as its final three digits.

This generalises: given any base n and any starting number a, the exponent tower a^(a^(a^...))) will eventually stabilize modulo n. After that point, whatever you put in the topmost exponent, be it just a last a, or a continuation of the exponent tower (i.e. more than one a), or any other number, its congruency class modulo n will not change. That is the challenge that I set before you here today.

## Problem statement

Write a program or a function that takes two numbers a and n (within your language's standard signed or unsigned integer range) as input, and outputs the limit l of the sequence a%n, (a^a)%n, (a^(a^a))%n,..., which can be mathematically proven to be eventually constant (and therefore have a well-defined limit).

Your program should be able to handle a > n (note that a and a+n doesn't necessarily give the same result), and we require that 0 <= l < n.

Warning: Reducing the exponents mudulo n, i.e. calculating this sequence recursively using b[0] = a%n, b[i] = (a^b[i-1])%n will yield the wrong result, and might not stabilize.

## Test cases

If we call the function f(a, n), it should give the following:

> f(3, 1000)
387
> f(6, 10)
6
> f(5, 9)
2
> f(14, 9)
4
> f(3, 81)
0


## Scoring criteria

Standard code golf rules, use as few bytes as possible.

# Voronoi Iteration

Given a finite set of points in the plane, output the set vertices of the corresponding Voronoi diagram.

### Details

A vertex of the voronoi diagram is a point of the plane that has the same distance to the three or more closest input points. As usual, you don't have to worry about the rounding issues of limited precision floating point numbers.

### Examples

[(0,0),(2,0),(0,2),(2,2)] -> [(1,1)]
[(0,0),(1,0)] -> []
[(0,0),(2,0),(0,2)] -> [(1,1)]


Inspired by this question on MO.

• I suggest having a test case with floating point coordinates. – user202729 Jan 22 '18 at 14:10
• (although I already understood the test cases) it would be helpful to have an image. – user202729 Jan 22 '18 at 14:16
• @user202729 It definitely needs more examples, but you can obviously interpret these coordinates as floating points as well. – flawr Jan 22 '18 at 14:17
• Having a test case with floating point coordinates will help testing if programs handle floating point input correctly. – user202729 Jan 28 '18 at 7:32

# Invisible target - probability KotH

## In short

Walls are gradually added and the player nearest to the stationary invisible target at the end of the game wins.

## Detail

Players are all present on a 32 by 32 grid of square cells, which wraps toroidally. One randomly chosen cell is the target, which is not indicated to any of the players (regardless of whether they are on that cell or not). The target does not move.

Players all take their turn simultaneously. After each turn there is a small chance of a wall being added.

### Wall rules

• The wall will never be placed on a player.
• The wall will never be placed in a cell that does not have a route to the target.
• Of the possible positions for the wall to be placed, one will be chosen uniformly pseudorandomly.
• The probability of a wall being placed each turn is 1/7.
• The wall will be placed such that every player still has a route to the target (this includes never placing a wall on the target).

Note that a player having a route to the target means that there exists a path that does not include a wall. If another player blocks the path it still counts as a path.

### Movement rules

• A player can move to any of the 4 orthogonally adjacent cells (or stay still).
• A player cannot share a cell with another player.
• A player cannot move onto a wall.
• A player can move onto the target, but will have no way of knowing that this has happened.

### Starting position

At the start of the game the arena will have no walls and the players will be randomly positioned with the guarantee that there are no other players within each player's 5 by 5 neighbourhood.

### Winning

Play will continue until no wall can be placed for 10 consecutive attempts (note that attempts only occur with probability 1/7 each turn so this will take more than 10 turns). When play stops the player closest to the target (by Manhattan distance) is the winner. Although this makes it possible to have an arbitrary number of joint winners, the density of walls by this point makes it unlikely there will be many, and in most cases there will be a player on the target cell, meaning only a single winner.

Each of the (one or several) joint winners scores one point. Games will be played until one player is the clear winner, or until it is clear there should be joint winners overall.

## Input and output

### Input

During an N player game the input will be a space separated string of N+1 integers received on STDIN:

• The player's position (an integer).
• The position of any wall added since the player's last turn (an integer).
• The position of every enemy player (N-1 integers).

Positions will be single integers from 0 to 1023, representing the distance in English reading order from the top left cell.

For a 4 by 4 arena this would give the following numbering:

 0  1  2  3
4  5  6  7
8  9 10 11
12 13 14 15


If no wall was added the wall location will be 1024.

During a particular game the order of enemy players will be consistent - the nth location will always refer to the same enemy player.

### Output

The player must send an integer from 0 to 4 to STDOUT representing a move in English reading order:

  0
1 2 3
4


(2 being no move).

A move to an unoccupied cell will not necessarily succeed - it will fail if another player is also trying to move to the same cell.

A move to an occupied cell will not necessarily fail - it will succeed if that player is also moving away from that cell (provided that player succeeds in moving away from that cell, and no other player is also trying to move to that cell).

This means two players can swap cells if they both decide to on the same turn.

A player taking longer than 50 milliseconds to respond will not move.

# Sandbox questions

• If someone can demonstrate that there can exist no better strategy than moving uniformly randomly, then I will not post this challenge. I'm hoping that the knowledge of the rules behind wall placement and the ability to block the movement of other players will make probability estimating competitive strategies non-trivial. This is answered - Nathan Merrill's strategy of moving to the reachable cell whose maximum distance to any other reachable cell is the shortest will beat the strategy of moving uniformly randomly (although in a crowded arena I don't believe this will be the best strategy so I still consider the question worth posting).

• Should this be tagged ? I am expecting answers to make use of probability theory, but I can't know in advance what all the strategies will be. Is this close enough to use the tag?

• I'm aiming for this to be a language agnostic challenge communicating with STDIN/STDOUT. Is there a language that is overdue to have its own language specific KotH contest, but that would still allow most users to participate? If not, I'll stick with language agnostic and include at least one example answer so that the processing of STDIN and STDOUT is provided in at least one language.

• Method for deciding which attempted moves succeed. Is there any problem with this: Make a list of every intended destination (including own current cell for non-movers). For any destination that appears more than once, make all players aiming for that destination aim for their own current cell instead. Repeat (as this may have created more clashes) until no change is made. Move all the players to the resulting destination. Guaranteed to finish in N steps per turn for an N player game (worst case being a chain of players each moving to the next player's current cell, with the last player in the chain attempting to move onto a wall).

• Pseudo random number source: Does anyone have a preferred/recommended random number generator? Is there any reason to consider a true random number source?

• Alternative adversarial 2 player version: One player is the target, and the other player is seeking the target. Each player can move one square orthogonally or stay still. Walls are added as in the multiplayer game, and the game ends when the seeker moves onto the target's cell. The score of each player is the number of moves the game lasted. Lower score is better for the seeker player, higher score is better for the target player. The target can always see the location of the seeker. The seeker can never see the location of the target. Might also be interesting to allow both players to choose where to place a wall on their turn (in addition to moving). This might open up the possibility of double bluff. Walls would still be prevented from being placed on a cell that doesn't leave a path from seeker to target. Would this be more/less interesting than the multiplayer version? Are they sufficiently distinct to post as separate challenges, or should one be chosen as the one to be posted? Would this adversarial version work best as two KotHs that use each other's answers to judge their own answers (like a cops and robbers challenge) or should all the seeker answers and target answers be posted to one challenge? Alternatively each answer could be required to deal with being either a seeker or a target, but I like the idea of people being able to specialise and build just one or other, without being obliged to write both.

• I believe the best strategy is to take all of the connected squares, and find the one that has the shortest walking distance to all other squares. Also, I think that walls should be placed every turn, as it appears to only slow down the game. – Nathan Merrill Jun 20 '15 at 0:18
• Also, I believe an interesting variant would be to have it more like the cats/mice KotH, where several mice compete to stand on the square first, and the cat tries to delay them as long as possible. – Nathan Merrill Jun 20 '15 at 0:21
• @NathanMerrill thanks for the feedback. When you say walls should be placed every turn, do you mean each time any player moves, or each time all N players have moved? – trichoplax Jun 20 '15 at 0:23
• Each time all N players have moved, although I wouldn't be against the other either. – Nathan Merrill Jun 20 '15 at 0:24
• Would the variant involve a cat that knows the position of the target? – trichoplax Jun 20 '15 at 0:24
• Yes, it would (wouldn't be interesting otherwise, I think) – Nathan Merrill Jun 20 '15 at 0:25
• @NathanMerrill my problem with adding the wall at the same point each time, after N players have moved, is that this means the players at the start of the cycle get first choice about where to move, which becomes more relevant in the later stages of the game. – trichoplax Jun 20 '15 at 0:26
• Then I would add a wall after N+1 players have taken a turn, or rotate the player's turns – Nathan Merrill Jun 20 '15 at 0:26
• That's an interesting idea - I'll consider changing it to that (N + 1 turns between walls) – trichoplax Jun 20 '15 at 0:27
• I'm not against several moves per player between walls though. I've chosen the arena small enough to allow a large number of moves in total, and the cell a player wishes to be on may be several cells away from the current cell, so I don't feel a strong need to add walls at high frequency. – trichoplax Jun 20 '15 at 0:30
• Moving to the center of the arena may well be worse than a uniformly random strategy ;) There's definitely one better than random though. – feersum Jun 20 '15 at 10:01
• Question: will player bots have information storage? That is, will a player be able to remember every wall that has been placed? – Draco18s Jul 29 '17 at 1:30
• @Draco18s yes the players will persist between moves, and can store information. I may place an upper limit on the amount of storage, but if I do it will be very generous. – trichoplax Jul 29 '17 at 1:36
• In which case, moving randomly is not the best strategy :) – Draco18s Jul 29 '17 at 1:38
• No, I'm thinking not, especially as a player can track what all of the other players are doing (they are distinguishable from each other, not just generic "enemy", but "player 1", "player 2", ...) – trichoplax Jul 29 '17 at 1:39

# Number rewinder

Inspired by this SO question and little bit expanded.

Your task is to rotate left a given integer by one digit in a given base and return integer (move the MSD to the LSD position).

Input: Two integers Number > Base > 1
Output: Result

Test cases:

Number Base  Result  String representations
61453   10    14536  61453 -> 14536
61453   16      223  F00D -> DF (00DF)
61453    8   229481  170015 -> 700151
60429   16    49374  EC0D -> C0DE
62977   16    24607  F601 -> 601F


This is Code-golf, standard loopholes are forbidden and shortest answer wins.

• I don't think your restriction about strings is going to work out well, there's not really a way to verify strings aren't being used. In any case, string rotation isn't that much different from the arithmetic required to do this operation. Personally, I'd recommend just allowing them. Thanks for using the sandbox! – FryAmTheEggman Feb 5 '18 at 22:09
• (i.e., we don't like do X without Y or unobservable behavior) – user202729 Feb 6 '18 at 5:45
• @FryAmTheEggman If there isn't some ToString-like function that opperates on any base using strings may be more difficult than dealing with it numerically. – Crowley Feb 6 '18 at 8:12
• I've never heard "rewind" used with this meaning before. I would call that operation "rotation left". – Peter Taylor Feb 6 '18 at 11:09
• @PeterTaylor Thanks for suggestion. I've updated bounds for the inputs to avoid rotating 1 digit "number" – Crowley Feb 6 '18 at 16:04

How acceptable is it to base challenges off of pre-existing challenges? I saw the challenge for Your Own Pet Ascii Snake and had a thought about making the output look more 'snakelike' by printing the characters |,\,/,(,),_ instead of always using the + character.

Here's how it would work. You would get some positive, negative, and 0 numbers as input, and based on those numbers, the snake moves one row down and that many characters in that direction. So, for a snake like the ones in the previous problem, your array would be restricted to the numbers 0, 1, and -1.

Here are the rules to draw the snake, the characters you print are dependent on the spacing of the lines before and after it.

So, say your snake is at position n (in the previous problem, n=30 to start, in this one you need to figure out a number for n that will keep your entire snake on the screen),

if the input is 0 you print n-1 spaces and a |
if the input is +1 you print n spaces and a \
if the input is +2 you print n spaces and \_, +10 would be \_________ (9 _ and a backslash)
if the input is -1 you print n-2 spaces and /
if the input is -2 you print n-3 spaces and _/, -10 would be _________/

Here's an example snake based on this array [+4, -3, +1, -4, +2, -3, +2, +5, -4, -1, -2, 0, +4, -4]

                        |
\___
__/
\
___/
\_
__/
\_
\____
____/
/
_/
|
\___
___/


I could also add optional 'curvy' rules that would include the '(' and ')' characters on direction changes to produce a snake like this, based on the same array above:

                         |
\___
___)
(_
____)
(__
___)
(__
\____
_____)
/
_/
(
\___
____)


note that for the curvy snake, 0s are handled differently depending on if there is a direction change in the rows above and below them, here there is a negative, 0, positive pattern, so we use a '(', if there were no direction change we'd use a |, and in the opposite pattern, a ')'

There are spaces to the left of my example snake because I didn't want to count out how many spaces I should leave exactly, I don't know whether it should be mandatory to cut out extra whitespace to the left, or whether to let people have as much or as little whitespace as they want, provided that their snake doesn't 'go off screen'

• I don't think there's a problem determining the next line randomly. For example, my program could generate the numbers for all 30 lines and then go back and format the characters appropriately. However, I'm not sure that's different enough to warrant its own challenge. Your second idea, though, regarding taking +1/-1/0 as input, that has some merit as it's pretty radically different than the existing snake challenge. – AdmBorkBork Feb 23 '18 at 19:29
• I'm far, far too tired for you to rely on my opinion alone but this looks sufficiently different enough from the 2 existing challenges to not be a dupe, once it's fleshed out a bit more. I'd suggest waiting a while before posting it, though, as people do get jaded of a barrage of similarly themed challenges. – Shaggy Feb 24 '18 at 21:26

The TI series of calculators. I've put a lot of hours in writing TI-BASIC programs. The single most tedious part was either scrolling through the program, or switching between alpha and numeric input.

For those unfamiliar, the entire Latin alphabet is overlaid on the existing keys alphabetically, and to type any of them (For variable names or assembly programming), you had to first press the ALPHA key, then your desired letter. Alternatively, you could press 2ND, A-LOCK and type in any number of letters, before pressing ALPHA again for numeric input.

Why am I saying all this? I want to write a code golf like challenge where scoring is done with this tediousness in mind, like switching between numbers/punctuation and letters carrying an extra penalty.

My original idea is that the source code of the submission would be converted to hexadecimal, and the number of transitions between alphas and numerics would be the "score," with a lower score being better.

How can/should I better refine this scoring system, and what sort of challenge should accompany it?

## The Challenge

Implement a program or function, in the language of your choice, that takes a string of characters as input and outputs that string's "tediousness score."

How tediousness is scored:

1. The string is converted into its hexadecimal representation. This is Unicode for languages that don't specify, but for a language like, say, Jelly, the Jelly codepage is used.
"The quick brown fox jumps, over the lazy dog's back." in Unicode == 0x54686520717569636b2062726f776e20666f78206a756d70732c206f76657220746865206c617a7920646f672773206261636b2e
2. Each switch between numbers and letters in the hexadecimal representation is counted.
0x54686520717569636b2062726f776e20666f78206a...
..0 12 34 56 78 9...
3. This is your tediousness score. For this example, it is 25.

Standard loopholes apply.

Should I change the tediousness score? How might I implement golf? I thought about adding/multiplying the two together, but it still seemed to be in favor of just plain golfing. I wanted to make golfing languages be a bit harder for a golfing challenge, since they really pack their character sets and there would be a high "tediousness score".

Is the challenge, as written, clear enough? Should I restrict or relax the I/O requirements?

• I have found that challenges with novel scoring mechanisms work nicely if the task is to implement the score calculator itself, see e.g. this challenge. – Laikoni Mar 12 '18 at 8:24
• Probably tedious×log(nbytes)? – user202729 Mar 13 '18 at 14:16
• What about giving a list of integers (byte values), or restricting the input to printable ASCII? – user202729 Mar 13 '18 at 14:29
• @user202729 Because I wanted entries to be scored by this method, and I didn't want to exclude esoteric golfing languages. I specifically want to include them, and make them hard to win with. – Orion Mar 14 '18 at 6:06
• What about "the input is a byte string"? That way you don't need to worry about the encoding. – user202729 Mar 14 '18 at 8:19

# Signed exponentiation

Let us define signed exponentiation of a base x to a power n as this procedure:

1. Take the absolute value of x.
2. Raise to the power of n.
3. Re-apply the original sign of x.

Or, for a more mathematical (albeit slightly flawed) definition:

For this challenge, we will denote the signed exponentiation of x to a as x ' a. Some notes:

• Unlike f(x) = xa, f(x) = x ' a is defined for negative x no matter the value of a.
• The negative portion of the graph of x ' n is the positive portion rotated halfway about the origin; hence, f(x) = x ' a is an odd function for all values of a.
• If a is odd, x ' a = xa for all values of x.
• x ' 1 = x, while x ' -1 = 1 / x. x ' 0 is a sign function (+1 for positive x, -1 for negative x).

## Challenge

Given a base x and a power n, compute x ' n.

### Rules

• You may assume that -9 ≤ x, n ≤ +9.
• You may assume that x ≠ 0, for the sake of avoiding 0 ' 0, 0 ' -1, etc.
• You may assume that 1e-4 ≤ |x ' n| ≤ 1e9.
• The output must be precise to at least 3 significant digits for the given test cases.
• Input/output may be taken/given in any standard format.

### Test cases

x, n -> output
1, 0 -> 1
3.14159, 0 -> 1
-9, 0 -> -1
7, 1 -> 7
-1.23456, 1 -> -1.23456
5, 2 -> 25
-4, 3 -> -64
0.1, 4 -> 0.0001
-9, 9 -> -387420489
1, -1 -> 1
-3, -1 -> -0.33333
5, -2 -> 0.04
2.71828, -9 -> 0.0001234
4, 0.5 -> 2
-2, 0.5 -> -1.41421
2, -0.5 -> 0.7071
3.8236, -1.6702 -> 0.10645
0.1, -9 -> 1000000000


## Scoring

This is , so the shortest code in bytes in each langauge wins.

# Sandbox questions

• Could the definition be improved?
• Too many test cases? Are there any important ones missing?
• Any issues with the rules?
• This isn't a huge deal, but I find the "your answer must be accurate to x significant figures" to be a largely unobservable property. The only ways to know that a submission meets this criterium is to check each and every possible combination, or to give an incredibly complex proof. I've always thought it was better to say floating point errors don't matter and to use loopholes otherwise. Maybe just a small thing about having to be able to represent any of the numbers from 1e-4 to 1e9? – FryAmTheEggman Oct 2 '17 at 21:23
• Thanks @FryAmTheEggman; I like your suggestion, but I'm afraid if it's not objective enough it'll cause any issues. Any suggestions on how to phrase it? – ETHproductions Oct 3 '17 at 21:38
• Perhaps have a few special test cases where they have to match the first three sig figs, and put in a line that those can't be hard coded. Then otherwise floating point errors don't matter? I'm honestly unsure. I've been getting to the point where I want to ask on meta because it always feels like fp questions are unclear or unobservable. – FryAmTheEggman Oct 4 '17 at 16:38
• @FryAmTheEggman Hopefully a little more objective now. – ETHproductions Feb 27 '18 at 1:54
• I think this looks much better, but there are perhaps too many "mandatory" test cases? Maybe making a split will make it easier for people to check the validity of answers. – FryAmTheEggman Feb 27 '18 at 6:04
• Am I allowed to print more than 3 sigfigs? – Nissa Apr 6 '18 at 22:02
• @StephenLeppik Of course. Should be slightly clarified now – ETHproductions Apr 7 '18 at 1:37
• The way to prevent hardcoding is to have hidden test cases. – user202729 Apr 7 '18 at 11:15
• @user202729 Not sure I understand. How could hard coding possibly be useful for this challenge? – ETHproductions Apr 7 '18 at 14:09
• "for the given test cases". Although, yes, normally it is not useful. Whether you think it's necessary is up to you, but I doubt anyone would do it. – user202729 Apr 7 '18 at 14:32

# Inversion languages

## Cops

For this challenge you will design two languages, A and B. Both A and B should be Turing equivalent1. When run in your two languages a program has four options:

1. It halts in both A and B.

2. It halts in A but not B.

3. It halts in B but not A.

4. It doesn't halt in either A or B.

Your goal is to try to design A and B such that as many programs as possible halt in exactly one language (options 2 and 3). Doing such for all programs is impossible2, thus there will always be programs that meet either criterion 1 or criterion 4. The robbers will attempt to find these programs.

### Further rules on languages

Since we are only considering whether programs halt or not we don't care about I/O. Because of this programs should not take any input. You may produce output but really doesn't matter because it can neither hurt nor help you.

All programs should be deterministic in both languages, this means that any program that can halt must always halt and any program that can run indefinitely must do so.

1. A concrete description of both languages

2. Proofs that each language as described is Turing complete.

Your definitions should be rigorous and unambiguous. Meaning that a reasonable person should (given enough time) be able to workout the result of any computation. This means all edge cases should be covered and there should be no undefined behavior.

### Scoring

Your score will be the time between your post and the first crack with a higher score being better.

## Robbers

Robbers will score 1 point for every answer that they crack, with a higher score being better.

Your answers should include the program which cracks the cop's answer and a proof that it does.

## Sandbox

This is kind of just an idea right now. I have to iron out a lot of details and I will. I'll flesh it out later I just want to get it down so I don't forget it. Right now the most useful feedback would be in broad strokes. Don't worry about details, that's my job.

1: Turing equivalent is very similar to Turing completeness, but also stipulates that the language can be simulated by a Turing machine. Turing complete languages are not Turing equivalent if they are incomputable.

2: Suppose that we did have two Turing complete languages A and B such that every program halted in exactly one of the languages. We could solve the halting problem in language A by running a program in both A and B on separate threads until one of them halted, then outputting whether it was A or not.

• +1, very nice idea. But "to maintain fairness, this challenge will only be open to submissions for one week after the first cop's answer is posted" doesn't make sense to me - it seems to make it less fair, by preventing anyone from competing who comes across the challenge late or just spends time on their submission. – Nathaniel Apr 3 '18 at 4:05
• @Nathaniel The problem is that answers are scored based on how long they last answers that are late to the party have a huge advantage, since people won't be monitoring the challenge as much the older it gets. I would love to have a challenge that is open indefinitely, I strive to make that for all my challenges, so if anyone can think of a objective winning criterion that allows for this I'm all ears. – Sriotchilism O'Zaic Apr 3 '18 at 4:08
• I see, hmm, that makes sense even if it's unsatisfying. Nothing comes to mind as an alternative scoring mechanism for this challenge for now. – Nathaniel Apr 3 '18 at 4:10
• A separate point: I wonder if this might be a bit hard for the cops. Off the top of my head, I find it hard to think of a way to design two languages such that it wouldn't be obvious how to crack it. This might just be a failure of my imagination, however! – Nathaniel Apr 3 '18 at 4:12
• What do you mean with input [a program] into your two languages? Is this about polyglots? If so, how would you consider programs which are syntax errors in one or both of the languages? – Leo Apr 3 '18 at 4:25
• @Leo Input should probably be replaced with the verb "run". This is about polyglots. This is one of the things I plan on expanding on later on, but I'll either disallow syntax errors or consider them to be halting. – Sriotchilism O'Zaic Apr 3 '18 at 4:34
• Maybe avoid encrypting? (If key doesn't match, A always halt and B never halt; you hve no key lol – l4m2 Apr 3 '18 at 5:23
• but once known turing complete it's usually easily converted to an ans – l4m2 Apr 3 '18 at 5:25
• Although languages A and B such that all programs halt in exactly one language is impossible, A and B such that can't find one is possible – l4m2 Apr 3 '18 at 7:24
• With respect to @Nathaniel's observation about "only open for a week", it's certainly true that one of the problems of C'n'R is that the robbers get bored or don't notice late cop submissions, but it's not clear what "open to submissions" means. You're surely not thinking of asking the mods to lock the question, so you can't stop people posting new submissions. Perhaps that would be better rephrased in terms of when you will award the "accepted answer". – Peter Taylor Apr 3 '18 at 8:47
• The issue of testability is also a big one. If B is something along the lines of "Run the program through A for N steps. If it terminates, enter an infinite loop. Otherwise take the parts which are comments in language A and run them." Tune N so that it takes about a week to get any program to terminate in B. – Peter Taylor Apr 3 '18 at 8:52
• @l4m2 I would rather not ban encrypting because I consider it an unenforcable restriction. As you pointed out proving an answer to be Turing complete becomes a large hurdle for cops to overcome if they choose to cryptography. For example it is unknown whether Malbodge Unshackled is TC. – Sriotchilism O'Zaic Apr 3 '18 at 17:00
• @tsh The problem with bubblegum or similar languages is that crypto functions are designed to be really hard to predict. This makes it hard to say anything concrete about their behavior, which in turn makes any language that uses them in a non-trivial manner, really hard to prove TC. TCness means it is possible to write a program for every Turing machine, and since it is almost impossible to write a program in the language it is hard to show that every program can be written. I would recommend trying to come up with a language pair that has these properties. You might run into some issues. – Sriotchilism O'Zaic Apr 8 '18 at 16:05
• @tsh There is no such thing as undefined behavior. – Sriotchilism O'Zaic Apr 9 '18 at 2:30
• Another couple of related questions: (1) to what extent does the interpreter have to meet the spec? Obviously it can't meet it completely, since the interpreter runs on a finite machine with finite addressing, and therefore can't technically be Turing complete. What about cases like integer overflow? (2) How would you handle bugs in the interpreter, and/or ambiguities in the spec? – Nathaniel Apr 9 '18 at 3:57

Really skirting bit of sandboxing here (I haven't taken the time to develop the question):

I'd like to do a 2-d variant of this one.

Two lasers between two mirrors

The input would be an ascii maze, with a marker for the laser starting point, e.g.:

+---+------+
|*  |      |
|   |      |
|   |  ----+
|   |      |
|   |      |
|   |      |
|   +---   |
|          |
|          |
|          |
+----------+

• Astrisk(*): laser starting point.
• Whitespace: passable.
• Any other character is a reflective obstacle.

Result:

+---+------+
|\  |   /\ |
| \ |  /  \|
|  \| /----+
|  /|/   /\|
| / |\  / /|
|/  | \/ / |
|\  +---/  |
| \    /   |
|  \  /    |
|   \/     |
+----------+


Rules:

• When you can't move horizontally, reverse horizontal direction.
• When you can't move vertically, reverse vertical direction.
• Stop going when you meet the same laser coming the other way (e.g. when you hit a corner or reach your starting position again).I'm thinking of a golfing challenge.
• If the laser revisits a space in the other direction, draw an upper case X.

Simplifying factors:

• Let's just say the laser always goes the same way.
• The map is always a rectangle.
• Just the one laser.

It'll probably just be a golfing challenge.

• What's the goal of the program, just to draw the path? Food for thought, if you wanted a related but different challenge you could include a "start" and "goal" marker, and make the program determine if the laser ever hits the goal, returning "true" or "false" instead of a drawn maze. Or perhaps it should return how many steps it takes to hit the goal, returning either an integer, or a falsy value if it never hits it? Up to you, but some ideas. – BradC Apr 11 '18 at 16:34
• Consider removing the outside wall. You say that the laser always goes in the same direction, but I think that you should explicitly say that it always starts heading south-east (or down-right). Important test cases: All of the walls aren't connected to the border. Laser hits a 1-length wall. Laser crosses itself. Laser hits a + (on the inside). Laser barely misses a +. Laser starts next a right wall. Laser starts next to bottom wall. Laser starts at a bottom-right corner. – Nathan Merrill Apr 11 '18 at 17:08

X1M4L got in before me and posted the very similar challenge Print the previous answer!, which I don't mind at all. However, that one seems to have turned out quite a lot more open-ended than this version would be, with answers tending to score in the tens of thousands. So after a sufficiently long delay this will probably not be considered a duplicate - I intend to leave it in the sandbox for at least a few months before posting.

This is an challenge. The first answer must output the empty string. The second answer must output the source code of the first answer, and so on, with each answer outputting the code of the previous one.

To make this challenging, no answer may be longer than 100 bytes in length. Once the answers start getting close to this limit, it will become necessary to compress the text of the previous answers, which itself will become harder over time.

Each answer should output the exact string of bytes that forms the previous program. Because of this, if your program is in any format other than plain ASCII, you should post a hexdump as well as the source, so that the next person knows exactly what to output.

An answer's score is its position in the chain, i.e. the Nth answer scores N points. Your score is the score of your highest-scoring answer. You are encouraged to treat this challenge cooperatively, keeping the chain going as long as possible by not adding extra unnecessary entropy to your code.

The code of your answer cannot be identical to the code of any previous answer. The first answer must be at least one byte in length.

You may not post two consecutive answers. There are no restrictions on language.

• that's so weird, I was thinking of this the other day, after seeing all those quine/answer chaining challenges. – geokavel Mar 21 '18 at 16:13
• You'd probably need to provide some non-empty seed, to prevent the answers from all being blank themselves. Also, would there be any restrictions on language choice - e.g. would each answer need to be in a different language than all those that came before? – Sok Mar 21 '18 at 16:29
• @user56656 just position in the chain - I've added it – Nathaniel Mar 22 '18 at 0:30
• @Sok I've fixed the "all programs empty" issue by requiring each entry to be different from the previous one. I tend towards not putting restrictions on language choice (I've added that for now) but if there's a good argument for including such restrictions I'm open minded. – Nathaniel Mar 22 '18 at 0:31
• You should probably prevent source reading. A pretty good strategy will to be to make a valid submission in language A that is also a period 2 quine in language B. Alternatively, you might want to impose the restriction that new answers are different from every previous answer instead of just the last one. – Sriotchilism O'Zaic Mar 22 '18 at 0:33
• Another consideration is whether consecutive answers should be permitted. It is pretty common to put restrictions on individual answerers, to prevent schemes designed to game the system. – Sriotchilism O'Zaic Mar 22 '18 at 0:35
• @user56656 I've implemented your idea about making them distinct from all previous answers, and I've banned consecutive answers by the same person. Does that cover all the bases? – Nathaniel Mar 22 '18 at 0:38
• I've also changed the length restriction to 100 (makes a shorter challenge, but the restriction will kick in sooner) – Nathaniel Mar 22 '18 at 0:39
• It might be prudent to try a test drive of the challenge (in chat) to test if the 100 byte limit is good. I'd be willing to help with that. Other than that I have no further thoughts at this time. – Sriotchilism O'Zaic Mar 22 '18 at 0:43
• @user56656 that makes sense - I'll try that when I have a chance (might be in a week or two). – Nathaniel Mar 22 '18 at 5:40
• I think you probably gain more from saying languages cannot be repeated (and including a stack snipped of used languages) than you do by adding a lot of workarounds for quines. I think it will cause the answers to become more interesting more quickly. It will also result in the challenge ending sooner, but given how the hello world answer chaining question went, I don't think you have too much to worry about with respect to longevity (though increasing the 100 may be a good idea if you decide to do this). – FryAmTheEggman Mar 22 '18 at 18:00
• @FryAmTheEggman I don't think quines will be a problem in any case, because the Nth answer has to output a program that outputs a program that ... that outputs the empty string, so by definition it can't be a quine. That could be got around with polyglots, but I'd be very surprised if it would be an issue in practice - the criterion of not being identical to a previous answer is there to prevent quines not only in practice but also in theory! – Nathaniel Mar 23 '18 at 0:59
• The problem that I see is that if languages are repeatable you might get a really boring and repetitive sequence of 3-4 languages that somewhat trivialise the problem appearing quickly after each more interesting answer. I perhaps should have said "trivial modifications of near-quines" instead? Anyway, this may not happen, but I think you should focus on this as well when doing the short test run (i.e. check what portion of answers can be trivially followed by a /// or Bubblegum program). – FryAmTheEggman Mar 23 '18 at 1:31
• How about making the maximum length of answer n a slowly growing function over n`? – Laikoni Mar 24 '18 at 10:43
• @Laikoni that's an interesting idea. I guess probably logarithmic would be good choice. I'll give it some thought. – Nathaniel Mar 24 '18 at 14:11