# Sandbox for Proposed Challenges

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

Sandbox FAQ

## Posting

Write your challenge just as you would when actually posting it, though you can optionally add a title at the top. You may also add some notes about specific things you would like to clarify before posting it. Other users will help you improve your challenge by rating and discussing it.

When you think your challenge is ready for the public, go ahead and post it, and replace the post here with a link to the challenge and delete the sandbox post.

## Discussion

The purpose of the sandbox is to give and receive feedback on posts. If you want to, feel free to give feedback to any posts you see here. Important things to comment about can include:

• Parts of the challenge you found unclear
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You don't need any qualifications to review sandbox posts. The target audience of most of these challenges is code golfers like you, so anything you find unclear will probably be unclear to others.

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## Other

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# Continuous Everywhere, Differentiable Nowhere

## Objective

Build the Weierstrass function $$\f(x) = \sum_{n=0}^\infty a^n \cos(b^n n x)\$$, where $$\a \in (0,1)\$$, $$\b\$$ is an odd positive integer, and $$\ab > 1 + 1.5\pi\$$.

## What's the fuss?

The Weierstrass function is an example of a function that is continuous everywhere, but differentiable nowhere.

## Format

Using floating-point number is permitted. Though it will be preferred to use a datatype that is able to represent arbitrary real numbers.

## Rules

$$\a\$$ and $$\b\$$ are up to your choice, as long as they satisfy the conditions.

For every $$\x \in \mathbb{R}\$$, evaluation of $$\f(x)\$$ must halt.

## Note

The fact that the function above is defined as an infinite series might seem to contradict the rule, but it actually doesn't. The Weierstrass function is computable, implying that it is possible to halt for every input. In particular, if it were to be implemented over floating-point numbers, it suffices to stop summing when the summand becomes denormal.

• I really doubt that the Weierstrass function is computable since its domain is real numbers and computer programs can only compute a select few functions on arbitrary real input. The Weierstrass function is very likely computable on some restricted domains like the rational numbers. Really this question has a some issues with the fact that continuity and differentiabilty are usually discussed in the context of real numbers, but does not require that it work on actual real numbers.
– Wheat Wizard Mod
Jul 16, 2020 at 1:36
• For example as it currently stands I could do something like just output the floating point zero regardless of input. This is approximates some cewdnw function, in fact it comes arbitrarily close to approximating an infinite number of cewdnw functions. For example just the Weierstrass function multiplied by a really small positive number.
– Wheat Wizard Mod
Jul 16, 2020 at 1:38
• However if you do restrict it to real numbers you run into the problem that very few functions are computable on real numbers. (The issue here is that a program on real numbers must be ready to accept an infinite string of input). I suggest restricting your domain to something like rational numbers, but note that this alters continuity and differntiability in subtle ways so it is not a simple patch.
– Wheat Wizard Mod
Jul 16, 2020 at 1:41
• Comment: while this problem is solvable in polynomial time, I guess the code-golf submissions are going to take exponential time. Jul 16, 2020 at 6:40
• @user202729 Do you actually have a polynomial tome algorithm?
– Wheat Wizard Mod
Jul 16, 2020 at 12:23
• Yes. -- -- -- -- -- -- Jul 16, 2020 at 13:29
• @user202729 What is it?
– Wheat Wizard Mod
Jul 16, 2020 at 13:34
• Iterate over substrings of the string, then check if it satisfies with f(left, right, prefix) = (can eraser[:prefix] be formed from string[left:right] by repeated erase operations?) At most this is O(n^6). Jul 16, 2020 at 13:38
• I cannot understand your notation so I do not understand your algorithm, but I will say it seems to me that checking whether an eraser erases a string should naïvely take O(2^n) since in strings like "ototoo" it matters which "oto" you erase first thus you have to branch between the possible choices.
– Wheat Wizard Mod
Jul 16, 2020 at 14:22
• The notation is like Python, string[left:right] is character from left..right (inclusive), eraser[:prefix] is eraser[0:prefix], characters are 0-indexed. Jul 16, 2020 at 14:32
• It's possible to compute each f(left, right, prefix) value from O(n) other values (dynamic programming) and there's only O(n^3) possible parameters. Jul 16, 2020 at 14:33
• @user202729 Ok, It looked like python but it didn't make any sense as python code, might you actually write this in python? It still doesn't make a whole lot of sense and even then feels like it should be O(2^n) because of "can [...] be formed from [...] by repeated erase operations?" seems to be an O(2^n) check to me.
– Wheat Wizard Mod
Jul 16, 2020 at 14:37
• f=lambda left, right, prefix: string[left:right]==eraser[:prefix] or (left!=right and (string[right-1]==eraser[prefix-1] and f(left, right-1, prefix-1) or f(left, right, len(eraser) or any(f(left, middle, prefix) and f(middle, right, 0) for middle in range(left+1, right)))), something like that, with caching. Jul 16, 2020 at 14:42
• Looks like this problem (or a similar one) has already appeared somewhere else. See codeforces.com/blog/entry/14090 Jul 16, 2020 at 14:46
• @user202729 Ok so I've spent a little while unpacking that algoirthm in the blog post and it seems to be O(2^n) unless there is some invariant I am missing. I will say I still do not have the slightest understanding of your algorithm.
– Wheat Wizard Mod
Jul 16, 2020 at 15:22
• About the blog: if you understood it then there is no way it can be 2^n because there are only n^2 different states (possible parameter values) of the dp function . Jul 17, 2020 at 2:44
• @user202729 The issue is that calculating a cell is not contsant time sometimes we are required to solve the entire problem again on a smaller string to fill in a cell. You can make schemes where the number of these cells is linear witht he size of the program, hence exponential time overall. however at this point I have found a dynamic programming algo that does this in O(n^4), so it doesn't matter much to me any more.
– Wheat Wizard Mod
Jul 17, 2020 at 3:23
• Now that this has been posted to main, could you delete this proposal to create more space for new answers? Sep 25, 2020 at 1:03

## Ant Storage Labyrinth code-golfmatrixarray-manipulationgrid

### Description

Using a simplified model, the place where ants store their food can be thought of as an $$\n\times n\$$ matrix. Each entry of the matrix is an integer that encodes how full that specific spot is, according to the following correspondence:

• 0 denotes an empty spot (the ants can add two more units of food),
• 1 denotes a half-filled spot (the ants can add one more unit of food),
• 2 denotes a filled spot (no more food can be stored in there).

Imagine an ant carrying $$\f\$$ units of food, that enters the "storage room" at a specific position (row $$\i\$$, column $$\j\$$ of the matrix). The ant can move one unit left, right, up or down with each step, and it can drop $$\2-q\$$ units of food at each spot it walks over (where $$\q\$$ is the initial capacity of that spot – either 0, 1 or 2 as described above). Your task is to find the length of the shortest path the ant can choose in order to store all $$\f\$$ units of food.

### Example

Let's say that the ant carries $$\4\$$ units and enters the following storage room ($$\6\times 6\$$ matrix) at position $$\(3,3)\$$ (1-indexed):

$$\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&1\\1&2&\color{red}{1}&2&1&1\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]$$

It drops $$\1\$$ unit right where it starts ($$\3\$$ left), then it has four optimal choices:

• 3 moves to the right, and 1 up,

$$\longrightarrow\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&1\\1&2&\color{green}{2}&\color{red}{2}&1&1\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]\longrightarrow\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&1\\1&2&\color{green}{2}&\color{green}{2}&\color{red}{1}&1\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]\longrightarrow\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&1\\1&2&\color{green}{2}&\color{green}{2}&\color{green}{2}&\color{red}{1}\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]\\\longrightarrow\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&\color{red}{1}\\1&2&\color{green}{2}&\color{green}{2}&\color{green}{2}&\color{green}{2}\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]\longrightarrow\left[\begin{matrix}0&2&2&2&2&2\\2&1&2&2&2&\color{green}{2}\\1&2&\color{green}{2}&\color{green}{2}&\color{green}{2}&\color{green}{2}\\2&1&2&2&2&2\\2&2&2&2&2&2\\1&2&2&1&2&2\\\end{matrix}\right]$$

• 2 moves to the left, and 2 up,

• 1 move up, 2 left, and one up,

• 1 move up, 1 left, 1 up, 1 left.

All of these require $$\4\$$ steps, so the final answer is $$\\boxed{4}\$$.

## Test cases

In progress. I need help coming up with interesting test cases / maybe a verification program.

# Error Once, Hello World Twice

Your task here is to write a Hello World program that, (no, this is not Do X Without Y!) contains two exact copies of the same string. to avoid trivial solutions like print "Hello World!"# your program must error out with only one copy.

This is code-golf, so shortest answer in bytes wins.

## Sandbox

• Wording?
• Tags?
• Length?
• Interesting enough to be posted?
• I double the source code, you print hello world? (I'm not saying this is a dupe, I'm asking if that accurately summaries the challenge.) Jul 25, 2020 at 11:28
• @Lyxal Yep. (15chars)
– null
Jul 25, 2020 at 12:04
• What if, rather than erroring out with one copy, make it so that it's valid if it prints out anything other than "Hello world"? Jul 30, 2020 at 16:40
• @Beefster Maybe... But that's probably not what I'm intending. I might consider later.
– null
Jul 31, 2020 at 10:25
• @HighlyRadioactive this also reminds me of my 2 cats in a quine challenge from a while ago. My main concern here is that "erroring out" is nebulous and different for every language. You could also make it so that the program must print nothing unless it's duplicated. Jul 31, 2020 at 16:13

# Successive operator sequences code-golfmatharithmetic

A successive operator sequence (made up terminology) is a sequence of the form $$\a(n + 1) = a(n) \text{ op } n\$$ where op cycles through a set of operators and $$\a(n)\$$ represents the $$\n\$$th term of the sequence.

For examples, if we set the operators to addition, multiplication and subtraction and $$\a(1) = 1\$$. then we will get the following sequence (which is also A047908):

a(1)                    = 1
a(2) = a(1) + 1 = 1 + 1 = 2
a(3) = a(2) * 2 = 2 * 2 = 4
a(4) = a(3) - 3 = 4 - 3 = 1
a(5) = a(4) + 4 = 1 + 4 = 5
a(6) = a(5) * 5 = 5 * 5 = 25


Write a program/function to output the $$\n\$$th term of a successive operator sequence given its initial term and operators.

• multiplication
• subtraction
• integer division (rounded towards negative infinity)

## Input Format

The operators are inputted as a string or array of character where each character represents an operator, you may choose your own mapping of character to operator.

## Scoring

This is so shortest bytes wins.

## Testcases

# first term, operators, n  ->  nth term
0,   ["+", "-", "*", "/"], 6   ->  4
1,   ["+", "*", "-"],      1   ->  1
1,   ["+", "*", "-"],      3   ->  4
1,   ["+", "*", "-"],      10  ->  199
1,   ["*", "+", "-"],      7   ->  -1
50,  ["*", "+", "-"],      1   ->  50
50,  ["*", "+", "-"],      4   ->  49
-10, ["*", "/", "-"],      5   ->  -32
-10, ["*", "/", "-"],      3   ->  -5
1,   ["+", "+", "*"],      5   ->  16
2,   ["+", "*"],           5   ->  36
0,   ["+"],                3   ->  3


Inspired by the sequence A047908

• Suggested test cases: only one operation; duplicate operations (like ["+","+","-"]); more than 4 operations. Also, should integer division round toward zero, toward negative infinity, or something else? Jul 18, 2020 at 19:10
• Does each string have to be one byte? Jul 19, 2020 at 19:26
• @fireflame, they have to be a single character not a single byte. Jul 20, 2020 at 15:23
• Why rounding division towards negative infinity? A lot of languages round integer division towards zero and this will add complexity just to do that. Notice that A047908 doesn't use division at all so why add it and make it a problem? Maybe even make it optional which way your answer does it as long as it's stated. Jul 27, 2020 at 17:59

# CoGo Rally

There's a game called Robo Rally, in which players "program" their robots five moves ahead, then simultaneously perform the moves, one at a time. The robots move over a "factory floor" grid, with the aim being to reach certain points on the board, in sequence, before the other robots do the same.

# Game Rules

For the purposes of this challenge, the rules will be simplified as follows:

• Each robot starts with 6 lives
• Each robot has a different, randomly assigned starting position (out of a fixed set of starting positions)
• The aim of the game is to reach all three checkpoints in the assigned order, before any other robot does the same.

## Movement Options

Each turn, your robot can make any one of the following movements:

• Rotate Clockwise 90 degrees
• Rotate Counter-clockwise 90 degrees
• Rotate 180 degrees
• Move Forward One
• Move Forward Two
• Move Forward Three [can only be used once until the next checkpoint is met]
• Reverse One (and stay facing the same way)
• Stay Still and gain 1 life, up to the maximum of 6

Your moves are pre-programmed in blocks of five, so choose carefully! The board may well be in a very different state in five moves time to what you think it will be.

Additionally, each movement is assigned a priority from 1-100. When you choose your block of five movements (you may use each movement any number of times, except the "move forward three", to form your five total movements) and the order they will occur in, you are also given five random numbers 1-100 to assign - one to each movement. Higher numbers will take priority where movements would cause two robots to enter the same space, for example.

## Board Items

The board contains the following items:

• Floor - the default tile on the board. No special effect.
• Walls - block a robot's path. If a robot moves forward or backward into a wall, it wastes that move (i.e. stays still, but doesn't gain a life). If the robot used "Move Forward Two", for example, it may be possible that the Robot can only move Forward One, and then stops infront of a wall, wasting the second part of the movement.
• Laser gun - fire in a straight line in a specific direction until they hit a wall or a robot. If a robot is ontop of a laser gun, it will be hit but the laser won't fire further. While moving forward two or three, a robot may pass over the path of a laser gun without being affected by it.
• Conveyor Belts - at the end of a turn (single movement option), a conveyor belt will move the robot one space in the direction the conveyor is pointing. Doesn't block lasers. Conveyor belts NEVER ROTATE ROBOTS, even if they move the robot in a different direction to the one it is facing. While moving forward two or three, a robot may move over a conveyor belt without being affected by it.
• Checkpoints (1,2,3) - act as a save point on the Robot's path and also heals all of a robot's lives and resets their use of the "Move Forward Three" action, the first time the checkpoint is visited. Checkpoints must be visited sequentially to be activated. Acts as a piece of floor in all other respects. Robots must END THEIR TURN ON THE CHECKPOINT, after interaction with other Robots; and not just pass over it.
• Holes - move the robot back to the previously visited checkpoint, or start position. Robot loses half its remaining life, rounded down. Holes act immediately, as soon as the robot enters the space - it doesn't wait for the "board interactions" part of the turn order.

## Interactions

Objects interact as follows:

• If a Robot moves into a space where another robot already exists, the other robot is shoved (moved) in the direction that the first robot was moving, one space; unless there is a wall or laser in the way. This effect may stack if multiple robots are in a line (i.e. all robots are shoved one space). This may cause a robot to fall into a hole or onto a conveyor belt.
• Moving off the edge of the board has the same effect as moving into a hole
• If a Laser fires and hits a robot, the robot stops the laser beam, and takes one damage.
• If a robot is facing another robot in a straight line with nothing blocking in between (i.e. no walls or other robots), the target robot takes 1 damage
• Therefore If two robots are facing towards each other with nothing blocking in between (i.e. no walls or other robots), both robots take one damage.

## Turn Order

1. determine (program) 5 movement options
2. determine Priorities (1-100) for these five turns
3. The programmed actions occur:
a. The first movement occurs for each player, in priority order from highest to lowest. Holes are acted on immediately (a robot cannot pass over a hole).
b. Robot Interactions are resolved (e.g. if one robot shoves another one)
c. Board Items act (lasers, conveyor belts, checkpoints)
i. If a robot loses all of its lives, it returns to the previous checkpoint (or start) with half lives (rounded up) and must sit out the remainder of the round d. Robots fire
i. If a robot loses all of its lives, it returns to the previous checkpoint (or start) with half lives (rounded up) and must sit out the remainder of the round e. Repeat for the remaining 4 movements
4. Repeat until one robot has reached all three checkpoints sequentially, or all robots have lost their lives

# The Challenge

Your robot must take the board (as a 2D array), and a seed for the Random number generator; and play the game on the given board.

The board is guaranteed to be solveable (there will always be a path from the start to each of the checkpoints)

# Sample Board

The above board would be represented in an array as follows:

[0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,LU,0,0,0,0,0]
[0,0,0,0,0,LL,2,LR,0,0,W,0]
[H,CL,CL,CL,CL,CL,CL,CL,CL,CL,0,0]
[0,0,0,0,0,CR,CR,CR,CR,CR,CR,H]
[0,W,0,0,0,0,0 ,0,0,0,0,0]
[0,W,0,0,0,0,W,0,W,0,0,0]
[1,W,0,0,0,0,CR,CR,CD,0,W,3]
[0,W,CR,CR,CR,0,CU,H,CD,W,0,0]
[0,LL,CR,CR,CR,CR,CU,CU,CL,0,0,0]
[0,0,S,S,S,S,0,0,W,0,0,0]


Where

Cx = Conveyor (x=Up, Down, Left, Right)
Lx = Laser gun (x=Up, Down, Left, Right)
S = Start
1,2,3 = Checkpoints
W = Wall
H = Hole
0 = Floor



# Sandbox Questions

Should this be , where you implement your robot in the least code possible; or , or something else? If KotH, I've never set one before so some advice would be appreciated!

• (if this is code golf) is it guaranteed that there exists a solution on every boards? Or only boards such that a solution exists are valid input? Jul 28, 2020 at 10:38
• Whether KotH or codegolf, the board will always be solvable (i.e. In all cases all of the checkpoints will be accessible, and there will be at least one path from any starting point to each of the checkpoints) Jul 28, 2020 at 10:40

# Paper folding. Posted HERE

• Now that this has been posted to main, could you delete this proposal to create more space for new answers? Sep 25, 2020 at 0:48

# The Dungeon Number Sequence code-golfnumberbase-conversion

### Introduction

The dungeon numbers are introduced by Numberphile, denoting a chain of base conversions. A dungeon number is denoted in the form $$a_{b_{c_{d_\cdots}}}$$ where all numbers involved are integers with at least two digits. When interpreting the values, each base conversion $$\a_b\$$ is treated as from base $$\b\$$ to base-10.

There are two types of dungeons, one starting from $$\10\$$ to $$\n\$$ from top to bottom, i.e. $$10_{11_{12_{\cdots_n}}}$$ increasing $$\1\$$ for each deeper layer, and one starting from $$\n\$$ to $$\10\$$ from top to bottom, i.e. $$n_{(n-1)_{(n-2)_{\cdots_{10}}}}$$ decreasing $$\1\$$ for each deeper layer. Each dungeon has two interpretations, top down, i.e. $$(((10_{11})_{12})_\cdots)_n$$, and bottom up, i.e. $$10_{(11_{(12_{(\cdots_n)})})}$$, producing 4 dungeon number sequences in total.

### Example

Considering $$10_{(11_{(12_{13})})}$$. The conversion is bottom up. First $$\12_{13}\$$ is converted to $$\15_{10}\$$. Then $$\11_{15}\$$ is converted to $$\16_{10}\$$. Finally $$\10_{16}\$$ is converted to $$\16_{10}\$$, and this is the value for $$\n=13\$$.

### Challenge

Write a program or function, given an integer $$\n>=10\$$ as input, output either the value of the dungeon number sequence at $$\n\$$, or the whole sequence from $$\10\$$ up to $$\n\$$ inclusive. You may choose any sequence from the 4 sequences, but you must state which you have chosen. You must not hardcode the values; your code must work theoretically for all integer $$\n>=10\$$.

### Values

n                                  10  11  12  13  14  15  16  17   18   19    20
---------------------------------------------------------------------------------
Type 1 (((10_11)_12)_...)_n        10  11  13  16  20  30  48  76  132  420  1640
Type 2 10_(11_(12_(..._n)))        10  11  13  16  20  25  31  38   46   55    65
Type 3 (((n_(n-1))_(n-2))_...)_10  10  11  13  16  20  28  45  73  133  348  4943
Type 4 n_((n-1)_((n-2)_(..._10)))  10  11  13  16  20  25  31  38   46   55   110


### Sample IO

• Type 1 ($$\(((10_{11})_{12})_\cdots)_n\$$)

15 => 30
20 => 1640
25 => 19563802363305

• Type 2 ($$\10_{(11_{(12_{(\cdots_n)})})}\$$)

15 => 25
20 => 65
25 => 943

• Type 3 ($$\(((n_{(n-1)})_{(n-2)})_\cdots)_{10}\$$)

15 => 28
20 => 4943
25 => 1092759075796059

• Type 4 ($$\n_{((n-1)_{((n-2)_{(\cdots_{10})})})}\$$)

15 => 25
20 => 110
25 => 3577


### Winning Criteria

This is a challenge, so shortest code for each language wins. No default loopholes.

# Posted: Antisymmetry of a Matrix

• Mathematica: AntisymmetricMatrixQ (of course, a non-built-in solution can be much shorter). Jul 30, 2020 at 13:12

# LaTeX Fractions

Inspired by a TeX SE question.

LaTeX uses \frac{a}{b} to represent a/b, which is very unintuitive. Now you have a piece of paper (as in "research paper") which happens to use the a/b format, and your task is to convert it to the LaTeX format.

[to be continued]

• @RahulVerma Nested fractions?
– null
Aug 10, 2020 at 13:17

# How Many Notches Are On Texas Red's Pistol?

The song, Big Iron, by Marty Robbins, is about an Arizona Ranger who rode into the town of Agua Fria to take the outlaw Texas Red alive (or maybe dead), armed with only the Big Iron (a .45 revolver) on his hip. Texas Red, despite being only 24 years old, is extremely dangerous, having already taken out 20 men who have tried to go after him. As a point of pride, he's carved out a notch on his pistol for each one. The song counts the notches on Texas Red's pistol as "one and nineteen more". After listening to the song a couple times, two questions crossed my mind:

2. What if the Ranger wasn't the 21st person to try?

## The Challenge

Given a positive integer, N, the total notches on Texas Red's pistol, and another number A (also an positive integer), output a number B such that B + A = N. In the context of the song, it should read "A and B more".

## The Catch

The song still has to be intact without sub-dividing any beats. That is, the number of syllables in the phrase "A and B more" must add up to 5. If it doesn't, output the string "oops". You may assume

• 0 < A < N < 20
• 1 < N

## Examples

N   A   B (output)

20  1   19   ("One and nineteen more.")
19  2   oops ("Two and seventeen more" has 6 syllables)
11  7   4    ("Seven and four more.")


## Syllable Counts

The numbers, from one to nineteen, have syllable counts as follows: one (1), two (1), three (1), four (1), five (1), six (1), seven (2), eight (1), nine (1), ten (1), eleven (3), twelve (1), thirteen (2), fourteen (2), fifteen (2), sixteen (2), seventeen (3), eighteen (2), and nineteen (2). No synonyms are accepted, such as "aught more" for "zero more".

## Scoring

: Shortest code in bytes wins. Standard loopholes apply.

### Meta Stuff:

I hope this is interesting enough. I thought just a normal subtraction problem would be too boring.

Is "oops" a good distinguishing output?

# Show an integer, in digits of your choice

## Input

A string representing digit characters, and a nonnegative integer.

## How?

We shall show the integer in positional notation, where the string has the digit characters. Assuming the string is zero-indexed, the $$\n\$$th character shall represent $$\n\$$. The length of the string is the base.

For example, "0123456789" will show the integer in the standard decimal representation.

## Rules

• The string is assumed to have at least 2 characters.

• Invalid inputs fall in don't care situation.

## Examples

Beware of the zero!

### Binary representation

Given "01" as the string:

$$\begin{array}{c|c} 0 & “0” \\ 4 & “100” \\ 8 & “1000” \\ 15 & “1111” \\ 16 & “10000” \\ 23 & “10111” \\ 42 & “101010” \end{array}$$

### Devanagari representation

Given "०१२३४५६७८९" (U+0966 – U+096F) as the string:

$$\begin{array}{c|c} 0 & “०” \\ 4 & “४” \\ 8 & “८” \\ 15 & “१५” \\ 16 & “१६” \\ 23 & “२३” \\ 42 & “४२” \end{array}$$

### Duodecimal representation

Given "0123456789↊↋" (The last two characters are U+218A and U+218B) as the string:

$$\begin{array}{c|c} 0 & “0” \\ 4 & “4” \\ 8 & “8” \\ 15 & “13” \\ 16 & “14” \\ 23 & “1↋” \\ 42 & “36” \end{array}$$

## Ungolfed solution

showIntArb :: String -> Int -> ShowS
showIntArb "" _ = error "showIntArb: No given digit"
showIntArb (d:_) 0 = showChar d
showIntArb ds n = let
appendDigit ints = if length ints <= n
then appendDigit $do d <- ds int <- ints return (d : int) else ints in showString (appendDigit (fmap return ds) !! n)  • so this is a base encoding question, with symbol replacement, right? Sep 14, 2020 at 17:43 • @Razetime Yes, exactly. Sep 14, 2020 at 22:51 # Haiku Quine A haiku is a type of poetry originating from Japan following a simple pattern: 5 syllables on the first line, 7 syllables on the second, and 5 syllables on the third. Traditionally, haikus also include some reference to nature or seasons, but we'll ignore tradition for the sake of this challenge. Your task is to create a quine which has some reasonable pronunciation in the form of a haiku. For example, consider this loophole-abusing (and thus non-competing) Python quine: 0+0 with open(__file__) as fp: print(fp.read())  To be read as: ze-ro plus ze-ro with o-pen file as F P print F P dot read  # Rules and Scoring This is , so the shortest code wins. • Standard rules and banned loopholes apply • Include a reasonable haiku pronunciation alongside your code (yes, this is inherently subjective and open-ended) NOTE: may be better as a • what's the standard for xxd output here? Sep 15, 2020 at 3:34 # Convert A String To Shorthand Shorthand has been used for hundreds of years to compress and speed up the speed at which someone can write down what is said. It does this using several abbreviating methods; three of which will be used here to compress a sentence. ## Challenge When given a sentence, alongside a set of 'briefs', 'prefixes' and 'suffixes' (defined below), print or return the sentence in its compressed form. ### Definitions • Brief: A word that can be entirely substituted by another string of characters. I.E. Would: D, Be: B, Able: Ab. "I would be able...": "I D B Ab • Prefix: The beginning of a word that can be substituted by another string of characters; the prefix will either be joined or dis-joined. After(Joined): Af. Afternoon = Afnoon. Enter/Inter/Intra(Dis-joined): N. Internet = N-net • Suffix: The ending of a word that can be substituted by another string of characters; the suffix will either be joined or dis-joined. ful/ify(Joined): F. Clarify = Clarf ification(Dis-joined): F. Clarification = Clar-f ### Input Structure 1. The first input will be the sentence to be converted 2. The second input is a collection of the briefs. Each brief is a collection itself, in which the first element represents the shortened form of that brief, while the rest of the elements are all strings that map to the brief. Example: [ [d, would], [m, much, more], [a, at, an] ] 3. The third and fourth inputs are collections of prefixes and suffixes. The first element of each prefix/suffix is the shortened form, the second element is a flag (of your choosing) that represents whether it is joined or dis-joined. Everything else are the strings that match the prefix/suffix. Prefix: [ [af, true, after], [n, false, enter, inter, intra] ] Suffix: [ [f, true, ful, ify], [f, false, ification] ] Sample Input: "a shipment of letters was delivered to the postshop", [["of", "o"], ["t", "to"], ["was", "os"], ["the", "th"]], [["sh", false, "ship"], ["d", true, "de"], ["po", false, "post"]], [["rs", true, "ers"], ["m", true, "ment"], ["d", true, "ed"]]  ## Rules, Assumptions and Freedoms • You may assume all input is lowercase letters. • A brief will always take priority over prefixes and suffixes. • you can indicate a dis-joined suffix/prefix however you wish, as long as you mention how you are indicating it. • The input may be rearranged however you like, as long as you specify how your input is structured • Output may be returned, printed or the nearest equivalent. ## Test Cases "a shipment of letters was delivered to the postshop", [["of", "o"], ["t", "to"], ["was", "os"], ["the", "th"]], [["sh", false, "ship"], ["d", true, "de"], ["po", false, "post"]], [["rs", true, "ers"], ["m", true, "ment"], ["d", true, "ed"]]  a sh-m o lettrs os dliverd t th po-shop "shorthand was once a common skill among woman", [["was", "os"]], [["sh", false, "ship", "short"], ["cm", true, "com"]], [["mn", true, "mon", "man"]]  sh-hand os once a cmmn skill among womn" "the electrician will be able to fix it", [["th", "the"], ["l", "will"], ["b", "be"], ["ab", "able"], "t", "to", "it"]], [["el", false, "electr"]], [["sh", true, "cian", "sion"]]  th el-ish l b ab t fix t • Looks like a nice challenge, I don't think there's much that needs to B clar-f-ed Sep 7, 2020 at 14:12 # Keep the symmetry SANDBOX: I am aware that the language in this challenge, as it stands, is quite... fluffy. If anyone could help me firm it up, I would be grateful. Also, would this be better as a cops-and-robbers style challenge, where the cops are trying to make the output more symmetrical, and the robbers make it less symmetrical? Given a 2D array of 1s and 0s, flip a 1 to a 0 and output the resulting array. The output array must be "closer to being symmetrical" than the input. In the case where the array is already symmetrical, it must still flip a 1 to a 0, breaking as little symmetry as possible - e.g for 1,0,1 1,0,1 1,0,1  In the above case, changing the top-left 1 to a 0 will break symmetry in both directions, whereas changing the middle-left 1 will only break symmetry one way. The output must be in the same form as the input (so that your program or function could take it in again). ### What is symmetry? I am talking about reflectional symmetry along both the horizontal and vertical axes. Where the array has an even number of entries in a row/column, the axis is between the two central rows/columns: 1,0,|,0,1 1,0,|,0,1 -,-,-,-,- 1,0,|,0,1 1,0,|,0,1  otherwise it's down the middle of the middle row/column (and the numbers in that row/column count on both sides).  | 1,0,1 -1,0,1- 1,0,1 |  ### Some Examples Each pair of grids below is input .. output, which then becomes the next input, etc. iteratively: 1,0,0,1 1,0,0,1 1,0,0,1 1,0,0,1 1,0,0,0 0,0,0,0 0,0,0,0 0,0,1,0 .. 0,0,0,0 .. 0,0,0,0 .. 0,0,0,0 .. 0,0,0,0 .. 0,0,0,0 .. 0,0,0,0 1,0,0,1 1,0,0,1 0,0,0,1 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0  1,1,1 1,0,1 1,0,1 1,0,1 1,0,1 1,1,1 .. 1,1,1 .. 1,0,1 .. 0,0,1 .. 0,0,0 1,0,1 1,0,1 1,0,1 1,0,1 1,0,1  • Is the program supposed to find the shortest path, or any path? Are we supposed to display each step? Should the choice of flipping a 1 to a 0 be random, or can it be calculated? A reference implementation would be very useful in this question. Aug 26, 2020 at 13:03 • The program is only supposed to flip one, calculated, bit from 1 to 0 and return the new grid. so iterative calls to the program would ultimately lead to all 0s. I guess I'm unclear exactly how I want the concept to be translated into a challenge, which is why I put the sandbox text at the top Aug 26, 2020 at 13:38 • The program must be trying to make the array symmetrical This needs to be defined precisely. What does it mean that the program "tries" to make it symmetrical? That repeated application of the program eventaully gives a symmetrical array? That it does it in a "small" (to be defined) number of steps? Same with as easy as possible: this needs to be defined precisely. I'm afraid I don't get the main idea of the challenge, actually Aug 26, 2020 at 17:21 # Balanced Beams Here are some examples of beams that balance: X Y A | X Y B Y --+-----+---+---+ | | | X X Y Y Y X X --+---- ----+-- + A X X Y | A B Y Y +---+---+-+-----+ | | | | B A | A AAB B A + --+-- --+-- + X Y X X | Y B X +-+-+---+---+---- | | | | Y A X Y Y X X X X + + + ------+----  The diagram will always be 17 characters wide and the top beam always balances in its centre. The other +s on the top beam indicate the point from which a lower beam hangs and the + on the lower beam indicates the point at which it balances. Your input does not need to include the |s if you don't need them. Lower beams with a width of 1 balance by default of course. The balancing of the top beam has to take the total weight of each lower beam into account. As you can see, for each example, there are two positions marked A and B where I have forgotten whether they should be an X or a Y. Please write a program a function which will accept the above diagram as input and output which of X and Y belong in each of the two positions A and B. Your output should be something along the lines of A=X, B=X although any unambiguous output suffices e.g. you could output the diagram with the A and B substituted accordingly or you could modify the input in-place. You do not have to output values for X or Y, although for each diagram they always have a fixed ratio which will allow all beams to balance. Other input formats could be acceptable but they need to get suggested as comments to the sandbox post. This is , so the shortest program or function that breaks no standard loopholes wins! ### Sandbox Question Do people think this is worth posting, given it only really requires a prime check along with getting digit prefixes? There are multiple implementations (possibly including hard-coding in some languages) to consider which might be enough. Please vote! Produce all 83 base-ten right-truncatable primes in as few bytes as possible in the language of your choice. • Order is irrelevant, but the production must terminate. • You may produce a list, a set, or an equivalent object. • You may print them (e.g. space-separated, each on a line, or formatted as a list or set (e.g. {2; 3; 293; 5; ...}) • You may give the numbers themselves as strings. • You may produce an iterator (but evaluating it must terminate). ### Right truncatable primes A right truncatable prime is a prime for which removing any number of trailing decimal digits is also prime. For example, $$\7193\$$ is a right truncatable prime since $$\719\$$, $$\71\$$, and $$\7\$$ are all prime. There are only 83 such numbers in base-ten, when sorted they are: [2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193, 31379, 37337, 37339, 37397, 59393, 59399, 71933, 73331, 73939, 233993, 239933, 293999, 373379, 373393, 593933, 593993, 719333, 739391, 739393, 739397, 739399, 2339933, 2399333, 2939999, 3733799, 5939333, 7393913, 7393931, 7393933, 23399339, 29399999, 37337999, 59393339, 73939133]  This is A024770 in the Online Encyclopedia of Integer Sequences. For some mathematician-written* Python see https://youtu.be/f2lEB4nMmyI. * Fair warning, it might well make you cringe. • I don't really mind prime challenges, just that most people who have been here a while have a stigma against it. Related. Sep 5, 2020 at 14:26 • The code in the link contains what appears to be a partially censored racial slur, so I think you should probably drop the youtube reference. Sep 9, 2020 at 21:32 • Otherwise I think this is probably interesting enough, as these primes have several other non-prime features. It might be problematic if too many answers are just primality checks wrapped in terminating loops, though? Sep 9, 2020 at 21:35 • @FryAmTheEggman Oh wow, I didn't notice; that's pretty sad. Sep 9, 2020 at 22:15 # Move the Knight! Your knight is on (0, 0) on an infinite (to all of the four edges, not just two) chessboard, and you need to move it to (a, b). You can use arbitrary (but finite) number of moves to do that. Since the chessboard is infinite, you can use squares with negative coordinates. Since you only have 2 knights (if no promotion occured) to type the program, your program needs to be as short as possible. ## Input The input is two integers, a and b. ## Output You output a sequence of characters, each represents a move. There are eight directions to move, so your output should contain eight distinct characters, each represents one direction. They can be any eight characters, as long as they are all unique. ## Test Cases The characters used here is:  A B C D N E F G H  0 0 -> "" 1 1 -> "GD" or "DEGD" or "DG" etc. 3 3 -> "DDDGGG" (one possible version) 2 3 -> "FGD"  ## Rules • Standard Loopholes are forbidden. • This is , so shortest code wins. • @Razetime I did... "They can be any eight characters, as long as they are all unique." – null Sep 15, 2020 at 12:30 • oh, sorry about that. Sep 15, 2020 at 12:31 • @Razetime I intend to make this challenge have many different, unique, interesting approach, and which one is shorter highly depends on the language. – null Sep 15, 2020 at 12:33 # Do my data follow Benford's law or a uniform distibution? ## Background Benford's law, also known as the law of anomalous numbers, describes the distribution of the leading digit in many numerical data sets. Let $$\X\$$ be the leading digit of an observation (in base 10). According to Benford's law, $$\P[X=i]=\log_{10}(1+\frac1i)\$$ for $$\i=1\ldots 9\$$. For instance take the yearly reputation change of the top 1000 users on CGCC. For a user with reputation change 3522, keep only the leading digit, 3. Repeat this for all users, and you get this distribution, which is far from uniform: This has been shown to apply to vary different data sets, from town populations to stock prices, and is used to detect tax and election fraud. On the other hand, for some other data sets, the distribution of the leading digit is a uniform distribution: $$\P[X=i] = \frac19\$$ for $$\i=1\ldots 9\$$. Given some observed frequencies $$\(f_i)_{i=1\ldots 9}\$$, we shall measure the distance to these two distributions using the sum of the errors in absolute value: $$\\sum_i \left|f_i-\log_{10}(1+\frac1i)\right|\$$ and $$\\sum_i\left|f_i-\frac19\right|\$$, respectively. ## Task Take as input a list of non-zero numbers. For each number, keep only the leading digit, which is defined as the first non-zero digit. Compute the observed frequencies of leading digits, and output one of two values, depending on whether the observed frequencies are closer to Benford's law or to a uniform distribution. ## Input Input format is flexible. Note that input may include negative values, as well as non-integers. ## Output Either two consistent values, one for Benford's law and one for the uniform, or a truthy/falsey value. ## Test cases To be added This is , so shortest answer in bytes wins. # Finding the densest crossword puzzles I love crosswords, and nothing beats a super densely packed puzzle. But how dense can the puzzles get? Here's a sample puzzle I made a few years ago: Certainly not great, but can we do better? Given any list of characters, a crosswordification of that list is a crossword puzzle consisting of characters from that list. For example, given the list ['b','a','d','a','d'], the following is a valid crosswordification: but this isn't Clearly, the order of the list is irrelevant. Given a valid crossword, the area of the crossword is the area of the smallest rectangle containing the crossword. In the above examples, the smallest rectangle containing the crosswords are 3x3 squares, which have area 9. # Challenge In this challenge, you must write a function which takes two arguments • A list-like structure containing english characters • A list-like of valid words consisting of english characters and outputs an integer, representing the minimal area of a crosswordification of the list of english characters, where the second input defines the set of valid words. I will be using this english dictionary for my test cases. Any code that is used to import/parse the dictionary into a list-like structure won't be counted in the byte-count, just the function. # Test Cases More to be added: ['d','a','a','a','t','n','m'] -> 7 (adamant is a word) ['k','a','s','a'] -> 6  • Here's what I understand: Our programs need to calculate the smallest possible corssword from the given characters, display the size alone. correct? Sep 17, 2020 at 5:04 • @Razetime correct Sep 17, 2020 at 13:51 • Do you suspect there is any other way to do this apart from brute forcing all possible arrangements and picking the minimal area one that meets the requirements? Sep 18, 2020 at 4:40 • @Sisyphus yes, but not revealing, as thats part of the challenge Sep 18, 2020 at 11:17 • "one or more of the options for the longest palindromic run of digits in its binary representation can be removed" Does this mean I can remove several runs? For example, 945770 = 11100110111001101010_2 has 110011 as the longest palindromic run, it occurs twice and if I remove both occurrences, the result is 10101010. On the other hand, 944522 = 11100110100110001010_2 has 110011 and 001100 as longest palindromic runs, and removing both gives 10101010. Sep 12, 2020 at 10:25 • Don't forget Dennis, Dennis 2.0 or Calvin numbers :P Sep 12, 2020 at 15:37 • @Zgarb No; you should only remove a single run before splitting the remaining digits. I've clarified this in the challenge text. Sep 13, 2020 at 0:50 ## The ASCII character countdown! answer-chainingrestricted-source Your task is simple: Choose any printable ASCII character that's not chosen in the previous answers. And then, you need to print your chosen character in your program to standard output. (You can ONLY print your chosen character, without printing other garbage to STDOUT) ## The catch Let's say you picked x as your chosen character, and your answer is the answer numbered y. You have to insert y x's into the previous source code, at any position you like. For the first answer, the previous answer is the empty program. ## An example Answers have to start with the number 1. So for example, I chose the character #, and I posted a 1 byte answer in /// that prints the # mark. #  And then, the second answer (numbered 2) has to insert 2 of their picked x character into the previous source code, such that the modified code will print their x character. So assume this is written in Keg: x#x  And then, the third answer has to do the same, and so on, until 95 is reached. ## The winning criterion & other rules • The first user whose answer stays without a succeeding answer for a month wins the challenge. If that's not satisfied, the first person who reaches the number 95 wins the challenge. • You are not allowed to put any other character in your code other than printable ASCII characters. • You need to wait for an hour before posting a chaining answer. • You need to wait 2 answers before you post a new answer after your submission. • Please make sure your answer is valid. If yours is not valid, chaining answers aren't allowed to be posted. • The answers are allowed to be in different languages. • Each submission doesn't have to be in a unique language. • You could only insert y x's into the source code. • Can the answers be in different langauges? Jul 20, 2020 at 4:03 • What is the motivation for the number 95? Jul 20, 2020 at 4:03 • This isn't a radiation hardening challenge, as those require programs to still work / do something different if any single character is removed. Jul 21, 2020 at 9:15 • @fireflame241 Because there are 95 ASCII characters of course... Jul 21, 2020 at 12:50 • Must we only insert y xs, or may we also insert other (printable ASCII) characters apart from our chosen character? If the latter, are the additional characters limited to those not already used in previous answers? Jul 21, 2020 at 15:02 • "I chose the character ?" -> "I chose the character #"? Jul 22, 2020 at 6:10 • "has to insert their picked x character into the previous source code," -> edit this part too. Jul 22, 2020 at 6:11 • @Dingus Now you may only insert y xs. – user92069 Jul 23, 2020 at 0:56 • "I chose the character ?" has crept back in. Other than that it's clear now. (Seems difficult too, but maybe not in the golfing langs - I don't know.) Jul 23, 2020 at 2:18 # Bit delivery in Bin Citycode-golfbinary posted • It could help a lot to add an illustration for small test cases (how to move each bit in the input to the output), and some test cases with more bytes (both even and odd). Other than that, looks good to me. Mar 31, 2020 at 1:57 • @Bubbler Thanks for the feedback. How's it now? Mar 31, 2020 at 14:32 • Perfect, and +1 for reference implementation. Mar 31, 2020 at 23:00 # Find a 3-Language Polyglot cops-and-robbers What I had in mind was that cops would create a polyglot with in 3 languages (languages A, B, and C). When run in A, the program would print the name of language B; when run in language B, the program would print the name of language C; and when run in C, it would print the name of language A. Cops have to provide the names of these 3 languages, as well as their original polyglot's characters scrambled in no particular order. as well as a valid program in A that has the same behavior as the polyglot (prints the name of B). This program must be able to be created by deleting characters from the original polyglot, i.e., all the letters in it are included in the hidden polyglot. Given the languages and the scrambled programand the sample program, robbers have to find the polyglot (or a polyglot that has the same behavior as the one the cop wrote). ## Rules • Any language chosen must be able to be run on TIO, repl.it, ideone, or someplace else online. If the language is obscure, please provide a link to some such website. • Any language used must have documentation on Esolangs, Wikipedia, GitHub, or someplace else. Unless the language is very commonly used and has tons of tutorials everywhere, such as Java, Haskell, or C, please provide a link to documentation. Any feature used in the program must be included in that documentation - it shouldn't be something people have to dig through layers of source code to find. Questions for meta: • Is this too easy/hard? Should I not include the extra A program? Should I only make it for 2 languages? • Is there anything unclear about the instructions? How can I improve the phrasing? • Should cops also give the length of their programs as an extra hint? • one thing to consider: you would need some way of restricting languages that are allowed. Otherwise people could just make up their own languages or use really, really obscure languages. Aug 18, 2020 at 23:04 • IIRC, the usual way to limit the language list is to specify "the language should be on at least one of Wikipedia, TIO, or esolangs.org", though esolangs is already crazy these days. Aug 19, 2020 at 5:05 • @Bubbler Yup, I've edited my question with some restrictions now – user Aug 20, 2020 at 15:01 # TPK Algorithm The TPK Algorithm was designed in 1977 Donald Knuth and Luis Trabb Pardo to show off the various functionality of languages at the time. Your task is to implement the most common version of the TPK algorithm. The pseudocode goes as follows (adapted from Wikipedia): ask for 11 numbers to be read into a sequence S reverse sequence S for each item N in sequence S call function F on N if the result is greater than 400 print "TOO LARGE" else print result F(N) results in sqrt(abs(N)) + 5 * pow(N,3)  F should be implemented as a function in your code, that is, there should be some subsection of you code which consists of a function that takes an input and outputs the result of F for that input. It is acceptable to round the square root operation down to the nearest integer. Notes: if using decimal square roots, the first value greater than 400 is ~4.301. For integer square roots, the first value is ~4.302. Your program does not need to support non-integer inputs. This is , so fewest bytes wins! # Three points on Poincaré disk ## What is Poincaré disk? Poincaré disk is a projection of 2-dimensional hyperbolic geometry to the 2-dimensional Euclidean plane, or more precisely, onto the open disk $$\\{(x,y): x^2 + y^2 < 1^2\}\$$. ## Objective It is well-known that three distinct points on the Euclidean plane are either on a unique line or on a unique circle. Let $$\S\$$ be that line/circle. The inverse image of $$\S\$$ is one of line, circle, horocycle, or hypercycle. Determine which. ## Classification The points are assumed to be on the disk. • If $$\S\$$ is a circle that lies on the disk, the inverse image is a circle. • Otherwise, if $$\S\$$ is a circle that shares a tangent with the boundary of the disk, the inverse image is a horocycle. • Otherwise, if $$\S\$$ crosses the boundary of the disk orthogonally, the inverse image is a line. • Otherwise, the inverse image is a hypercycle. ## Input The cartesian 2-dimensional coordinates of the points. A coordinate can be given as either two real numbers or one complex number. Other than that, the input type and format doesn't matter. This includes: • A tuple of size 3 • A list of size 3 • A set of size 3 Invalid inputs fall in don't care situation. This includes: • Not exactly 3 points • Non-distinct points • A point not on the disk ## Output Output type and format doesn't matter either. This includes: • Enumeration type of 4 possible values • Bit field of size 2 ## Example Assuming there were no floating-point errors: • $$\\{(-½,0),(0,½),(½,0)\}\$$ must give a circle. • $$\\{(-½,½),(0,0),(½,½)\}\$$ must give a horocycle. • $$\\{(-½,0),(0,0),(½,0)\}\$$ must give a line. • $$\\{(1-\sqrt{¾},½),(1-\sqrt{½},1-\sqrt{½}),(½,1-\sqrt{¾})\}\$$ must also give a line. • $$\\{(0,½),(¼,¼),(½,0)\}\$$ must give a hypercycle. • $$\\{(0,0),(¾,0),(0,¾)\}\$$ must also give a hypercycle. • Can the coordinates $(x,y)$ be represented as a complex number $x+yi$? Oct 11, 2020 at 16:43 • @cairdcoinheringaahing Yes. Oct 11, 2020 at 21:02 • It looks like solutions might have trouble with the line and horocycle cases due to float precision, if either they take values like sqrt(2) to finite precision or introduce imprecisions in the calculations. Can some allowance be made for this? I'm not sure how though. – xnor Oct 12, 2020 at 2:09 • @xnor If the input is IEEE floating-point numbers, they are in $\mathbb{Z}[½]$ anyway and must be regarded as such. If your language is able to do symbolic computation, you may go ahead. Oct 12, 2020 at 3:15 # Compactify the real numbers to a group (WIP) ## Objective Let $$\X = \mathbb{R} \cup \{\infty\}\$$. The $$\\infty\$$ is the point at infinity and doesn't have a signature. Let $$\Y = \{\exp(i\theta) : \theta \in [0,2\pi)\}\$$, which is the unit circle on the complex plane. Make $$\X\$$ a group by giving $$\X\$$ a binary operation, so there will exist a function $$\f : X → Y\$$ that is both an isomorphism and a homeomorphism. Your code shall implement the binary operation. $$\f\$$ doesn't need to be implemented to a code. ## Group A set $$\G\$$ endowed with a binary operation $$\*\$$ is a group iff: • For every $$\a,b,c \in G\$$, $$\(a * b) * c = a * (b * c)\$$ • There exists the identity element $$\e \in G\$$ such that for every $$\a \in G\$$, $$\e * a = a * e = a\$$ • For every $$\a \in G\$$, there exists $$\b \in G\$$ such that $$\b * a = a * b = e\$$ $$\Y\$$ is a group, where the binary operation is the multiplication. ## Isomorphism Let $$\*\$$ denote the binary operation given to $$\X\$$. A function $$\f : X → Y\$$ is an isomorphism iff: • $$\f\$$ is bijective • For every $$\x,y \in X\$$, $$\f(x*y) = f(x) × f(y)\$$ Note that once appropriate $$\f\$$ is identified, $$\*\$$ can be automatically defined as $$\x * y = f^{-1}(f(x) × f(y))\$$. ## Topology A subset $$\A \subset X\$$ is open iff, for every $$\x \in A\$$: • If $$\x \in \mathbb{R}\$$, there exists $$\P \subset A\$$ such that $$\x \in P\$$ and $$\P\$$ is an open interval • If $$\x = \infty\$$, there exists a subset $$\P \subset A\$$ such that $$\x \in P\$$ and $$\P\$$ is the union of two open rays to the opposite directions A subset $$\B \subset Y\$$ is open iff, for every $$\y \in B\$$, there exists a subset $$\Q \subset B\$$ such that $$\y \in Q\$$ and $$\Q\$$ is an open arc. ## Homeomorphism A function $$\f : X → Y\$$ is a homeomorphism iff: • $$\f\$$ is bijective • For every open subset $$\A \subset X\$$, its image $$\f[A]\$$ is open in $$\Y\$$. • For every open subset $$\B \subset Y\$$, its inverse image $$\f^{-1}[B]\$$ is open in $$\X\$$. ## Rule You may represent $$\\mathbb{R}\$$ as a floating-point number. Every floating-point error will be tolerated in this regard. ## Example An example of $$\f\$$ is: $$f(x) = \exp(i × 2 \arctan \frac{x}{2})$$ where $$\\arctan \infty = \frac{\pi}{2}\$$, and we identify $$\*\$$ as: $$x * y = 2 × \tan (\arctan \frac{x}{2} + \arctan \frac{y}{2})$$ where the identity element is $$\0\$$, and the inverse element of $$\x\$$ is $$\-x\$$ when $$\x \in \mathbb{R}\$$, or $$\\infty\$$ if $$\x = \infty\$$. ## Ungolfed solution ### Haskell This implementation abuses the fact that IEEE floating-point numbers can encode infinities. Both positive infinity and negative infinity will be treated the same in this regard. import Data.Semigroup import Data.Monoid import Data.Group newtype CompactR = CompactR Double deriving (Eq, Show, Read) instance Semigroup CompactR where CompactR x <> CompactR y = CompactR$ 2 * tan (atan (x/2) + atan (y/2))

instance Monoid CompactR where
mempty = CompactR 0

instance Group CompactR where
invert (CompactR x) = CompactR (negate x)


You implement only <>. The others are just details.

# Sandbox questions

This challange turned out to be too easy.

What if I asked about one-point compactification of $$\\mathbb{C}\$$ instead of $$\\mathbb{R}\$$?

• I think even just f(x,y)=(x+y)/(1+xy) works for the real case
– xnor
Oct 14, 2020 at 8:01

We have a lot of base conversion challenges. Surprisingly, aside from one closed challenge, there aren't any where the goal is purely to convert hexadecimal to decimal. This is different from challenges like converting hexadecimal to binary, because many languages have features like hexadecimal literals (0x, \$, etc.) which can do this in a much shorter or more interesting way.

I/O:

You should create either a program or function, which takes input and output through one of the allowed methods. The input will be a hexadecimal number, consisting of the characters /[0-9a-f]/` (you may choose the capitalization rules).

Scoring:

This is code golf, shortest answer per language wins.

• Feedback is of course useful. If the downvote is because this is a dupe or is unnecessary, that would be useful to comment on. Otherwise, I can't fix any issues without knowing what they are. Oct 17, 2020 at 21:11

# Recolour my Table (Abandoned)

• Maybe try limiting the table format. Is it top down or sideways? Also can we assume that the original table color (or slight variation to a certain HSL difference, maybe) is the majority of the image? Feb 6, 2020 at 19:50