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3633 Answers 3633

31 32
34 35

Find the k-th order summary of a number


  • \$\begingroup\$ very similar: codegolf.stackexchange.com/questions/70837/say-what-you-see \$\endgroup\$
    – Razetime
    Nov 4 '21 at 2:15
  • \$\begingroup\$ @Razetime, yes they are quite similar, but the look and say operation is a bit different from the summary operation; for example look_and_say(112211) = 21 22 21 whereas summary(112211) = 41 22 \$\endgroup\$ Nov 4 '21 at 5:51

Consider all arrays of \$\ell\$ non-negative integers in the range \$0,\dots,m\$. Consider all such arrays whose sum is exactly \$s\$. We can list those in lexicographic order and assign an integer to each one which is simply its rank in the list.

For example, take \$\ell=7, s=5, m=4\$, the list could look like:

(0, 0, 0, 0, 0, 1, 4)  rank 1
(0, 0, 0, 0, 0, 2, 3)  rank 2
(0, 0, 0, 0, 0, 3, 2)  rank 3
(0, 0, 0, 0, 0, 4, 1)  rank 4
(0, 0, 0, 0, 1, 0, 4)  rank 5
(0, 0, 0, 0, 1, 1, 3)  rank 6
(0, 0, 0, 0, 1, 2, 2)  rank 7
(0, 0, 0, 0, 1, 3, 1)  rank 8
(0, 0, 0, 0, 1, 4, 0)  rank 9
(3, 2, 0, 0, 0, 0, 0) rank 449
(4, 0, 0, 0, 0, 0, 1) rank 450
(4, 0, 0, 0, 0, 1, 0) rank 451
(4, 0, 0, 0, 1, 0, 0) rank 452
(4, 0, 0, 1, 0, 0, 0) rank 453
(4, 0, 1, 0, 0, 0, 0) rank 454
(4, 1, 0, 0, 0, 0, 0) rank 455

This challenge requires you to produce two pieces of code/functions.

  • Given a rank, compute the corresponding array directly. Call this function unrank()
  • Given an array, compute its rank. Call this function rank()

Your code should run in polynomial time. That is it shouldn't be brute force and more specifically it should take \$O(\ell^a s^b m^c)\$ time for fixed non-negative integers \$a, b, c\$. Any non-brute force method is likely to satisfy this requirement.


unrank((7, 5, 4), 9) = (0, 0, 0, 0, 1, 4, 0)
rank((7, 5, 4), (4, 0, 0, 0, 0, 1, 0)) = 451
unrank((14,10, 8), 100000)  = (0, 0, 0, 1, 0, 0, 1, 3, 1, 2, 0, 0, 2, 0)
rank((14, 10, 8), (2, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 0)) = 1000000

Your score will be the total size for your code


Convert codepoint to UTF-9

  • 5
    \$\begingroup\$ For clarity, I'd start octal constants with 0o. Also, an explanation of how UTF-9 works should probably be included here. \$\endgroup\$ Jun 19 '21 at 1:39
  • 2
    \$\begingroup\$ Could you include the basic algorithm to encode UTF-9 in your post instead of require an external resource? So this question can be made self contained. \$\endgroup\$
    – tsh
    Oct 12 '21 at 6:27
  • \$\begingroup\$ @tsh Should I do with actual program source or in pseudo code? \$\endgroup\$
    – user100411
    Oct 12 '21 at 12:26
  • \$\begingroup\$ first challenge that made me LOL \$\endgroup\$
    – don bright
    Oct 18 '21 at 3:12

Lexigolf: Is this number a prime?

Write a program that, given a strictly positive integer n as input, determines whether n is prime and prints a truthy or falsy value accordingly.

For the purpose of this challenge, an integer is prime if it has exactly two strictly positive divisors. Note that this excludes 1, who is its only strictly positive divisor.


Competing programs are compared lexicographically. The program that is lexicographically less than all other programs is the winner.

If a program begins with a prefix that may be removed without altering the program's behavior, it is disqualified. This is to discourage adding meaningless whitespace or comments to change the first character (consider int main(){} or /**/int main(){}).

For example,

abc < def
aa < ba
aaaaaaa < aba
aa < aaaa
Zzz < aaa
012 < AAA


This is essentially an earlier classic code-golf challenge, Is this number a prime?, except with a different goal, which I propose is called lexigolf.

I'm not sure whether lexicographic order should entirely be based on UTF-8 (for languages that can be expressed in bytes). It seems to massively favor weird esolangs that rely on characters with small ASCII codes. There is also a loophole in prefixing the program with noop characters, e.g. placing a arbitrary amount of whitespace before a C program: int main() {} > int main(int, char**) {} > int main(int argc, char **argv) {} (fixed? probably still a loophole somewhere)

  • 1
    \$\begingroup\$ For the scoring favoring weird esolangs that rely on certain characters, the scoring here is typically a per-language comptition, so Java and GolfScript wouldn't be competing. The null byte prefixing is a bit of an issue, so you might want to require that you can't take any number of characters off the left side of the program without making it stop working (so prefixing a null byte wouldn't be allowed unless it actually affected how the program ran). Also, primality testing might not be the best challenge for this idea, since many golfing languages have it as one or two byte built-ins. \$\endgroup\$ Nov 16 '21 at 17:42
  • \$\begingroup\$ @Fmbalbuena The < are to indicate which is lexicographically smaller, not which is winning \$\endgroup\$ Nov 16 '21 at 17:43
  • 2
    \$\begingroup\$ You might want to allow language with SBCSs (custom code pages, instead of UTF-8 or ASCII) like Jelly to use those for the lexicographic order instead, since that would make it more interesting to try to find the lexicographically smallest program in those languages. \$\endgroup\$ Nov 16 '21 at 17:46
  • \$\begingroup\$ @RedwolfPrograms, I've updated the post \$\endgroup\$
    Nov 16 '21 at 17:51
  • 1
    \$\begingroup\$ In some languages (for example, Befunge) you could probably detect whether the leading spaces were removed... \$\endgroup\$
    – NieDzejkob
    Nov 16 '21 at 22:19
  • 3
    \$\begingroup\$ Removing only prefixes isn't enough: I could add a test at the end to check whether that prefix is present. Maybe you should require the code to be irreducible instead? \$\endgroup\$
    – Dingus
    Nov 16 '21 at 22:55
  • 4
    \$\begingroup\$ It seems like this challenge is entirely about finding the lexicographically smallest prefix that can be extended arbitrarily far in a way that removing a prefix of it will be invalid syntax or fail. The prime-finding task doesn't really matter -- any code is equivalent if put after arbitrarily much prefix padding. \$\endgroup\$
    – xnor
    Nov 17 '21 at 2:12

Will one-cell brainfuck halt?

  • 3
    \$\begingroup\$ Do you really want use - for increment while + for decrement? Or maybe a typo? \$\endgroup\$
    – tsh
    Nov 10 '21 at 10:17
  • \$\begingroup\$ @tsh Oops. Fixed. \$\endgroup\$
    – emanresu A
    Nov 14 '21 at 1:01

Construct a Heptagon avoiding compass use

A while back I asked you to construct a pentagon avoiding compass use. Now flawr suggested:

Next time you should ask people to draw a heptagon, which would be slightly more challenging:)

This is of course a joke, because if you didn't already know it is not possible to construct a Heptagon using a ruler and compass ...

... in finite steps.

In this challenge answers will construct equilateral polygon of 7 sides, using a ruler and a compass.

We will begin with some standard ruler and compass operations:

  • Draw a line that passes through two non-identical points. (Ruler)

  • Draw a circle centered at one point such that another point lies on the circle. (Compass)

  • Place a point at an intersection of two non-identical objects (a circle and a line, a line and a line or a circle and a circle)

Normally a construction must be finished after some finite number of operations. However we will allow you to take any ordinal number of steps. Meaning you can perform an infinite number of steps and then perform more.

To go with this you are given one more operation:

  • Choose converging sequence of already drawn points and place a point at their limit. (limiting)

This operation is only meaningfully useful if you have already performed an infinite number of steps, but is crucial to constructing a heptagon.


In this challenge you will start with two arbitrarily placed (but non-equal) points on an infinite plane. You must then describe some sequence of steps to arrive at a regular Heptagon. Here a regular heptagon simply being 7 points which form the vertices of a heptagon, they do not need to be in any particular position relative to the starting points.

Your score will be the number of compass operations used in the entire proof with lower being better. Since many answers may end up using an infinite number of compass steps we will break ties by the strict supremum of ordinals representing steps you have used a compass.

For example if two answers both use an infinite number of compass operations, their primary score is \$\infty\$. If one of them uses all of their compasses at finite numbered their secondary score is \$\omega\$, which would beat the other answer if it uses the compass at any time \$\omega\$ and after.

  • 1
    \$\begingroup\$ The theoretical optimal score is likely 2. It is known that a circle and its center (with a couple other known points, because we can't create arbitrary point) plus straightedge operations equals general compass + straightedge in terms of constructibility. It must be possible to construct a sequence of constructible points that converges to a heptagon-related point. The actual challenge is coming up with a constructive solution. \$\endgroup\$
    – Bubbler
    Dec 6 '21 at 2:01

Sum powers to n

Posted to main


How long will my microwave run for?

  • \$\begingroup\$ I'd recommend getting rid of the bonuses, they're pretty strongly discouraged \$\endgroup\$ Dec 3 '21 at 17:32
  • \$\begingroup\$ @RedwolfPrograms I do like the bonus challenge, however I'm not sure what to do with it. \$\endgroup\$ Dec 3 '21 at 17:33
  • 1
    \$\begingroup\$ You could just turn the bonus challenge into a separate question \$\endgroup\$
    – pxeger
    Dec 3 '21 at 17:41
  • \$\begingroup\$ @pxeger I'll make it a seperate question and post it later. \$\endgroup\$ Dec 3 '21 at 17:49

Operator precedence is dead

Calculate the result of some math expressions using the following constraints:

  • Numbers will be between 0 and 9
  • Operators are + - / *
  • Expressions will always have the format Number operator number operator number...
  • Parenthesis have the highest precedence
  • The order of reading goes Left Left Right Right Left Left Right Right etc.
  • Division by 0 never happen

For example:

1       = 1   ; Start calculating using the left most number
 +    9 = 10  ; Add 9
  3  *  = 30  ; Multiply by 3
   -4   = 26  ; subtract 4

Using this method 1+3-4*9 = 26

Input / Output


  • string OR list of characters OR list of numbers and characters
  • Can be reversed if specified in the answer

Output: a number


Floating point errors are OK.

More examples and test cases:

2*9 = 18
1       = 1
 +    9 = 10
  3  *  = 30
   -4   = 26
8               = 8
 -            4 = 4
  5          *  = 20
   *        3   = 60
    0      +    = 60
     /    2     = 30
      9  /      = 3.33333...
       +8       = 11.33333...
Knowing that 1+3-4*9 is 26

8                       = 8
 -                    4 = 4
  5                  *  = 20
   *        (1+3-4*9)   = 520
    0      +            = 520
     /    2             = 260
      9  /              = 28.8888...
       +8               = 36.8888...
8         = 8
 -      2 = 6
  2    /  = 3
   +  6   = 9
    4*    = 36

First group:
 +  7 = 8
  2*  = 16

Second group:
 *  3 = 6
  2+  = 8

(1+2*7)             = 16
       *    (2*2+3) = 128
        6  +        = 134
         +3         = 137
Nested group:
6     = 6
 +  2 = 8
  1*  = 8

6           = 6
 +        2 = 8
  (6+1*2)/  = 1

Full expression:
1                 = 1
 +              4 = 5
  (6+(6+1*2)/2)/  = 5


This is , so the answer with the least amount of bytes wins.

  • 1
    \$\begingroup\$ "Division by 0 should not return a valid number." What do you mean by "a valid number"? I'd suggest just saying answers can assume division by zero will never occur \$\endgroup\$
    – pxeger
    Dec 17 '21 at 3:05
  • 1
    \$\begingroup\$ Thanks for your feedback @pxeger ! I'm removing errors handling \$\endgroup\$
    – Julian
    Dec 17 '21 at 3:20

Subdivide the Bezier Curve


A Bezier curve is a type of curve that has a lot of applications in all sorts of places, but most commonly, in computer graphics. It has a very simple algorithm and yet can represent a wide variety of shapes with just one common formula. If you've ever used pen tools in drawing software, you're probably already familiar with the general idea behind Bezier curves.

Given an ordered list of control points, we set some parameter \$t\$ in the range \$[0, 1]\$. Then, for each \$t\$, we draw a line between each consecutive pair of control points and select a point that is \$t\$ from the starting point. For example, if we have three control points and \$t\$ is \$\frac13\$:

enter image description here

The purple point is \$\frac13\$ of the way from the red point to the blue point, and the black point is \$\frac13\$ of the way from the blue point to the green point. You can change the ratio and move the points around here to try it out.

Now, we have one fewer point than we initially had control points. Let these be the new control points, and do this again with the same \$t\$:

enter image description here

(Desmos link). Now, we finally have a single point, so that is the point we obtain for this value of our parameter \$t\$. The Bezier curve is obtained from all final points for each \$0\leq t\leq 1\$. For more points, we just repeat this for more steps. Here's what a Bezier curve with four control points looks like:

enter image description here

(Desmos link)


Given a list of control points for a Bezier curve and a positive integer \$n\$, subdivide the Bezier curve into \$n\$ segments and return the points. More precisely, return the output points for \$t=0,\frac1n,\frac2n,\cdots,\frac{n-1}n,1\$.

You may do I/O in any reasonable format; for example, a list of pairs or a pair of x and y coordinates for input, and a pair of numbers for output. Floating point errors are acceptable but your outputs should have an accuracy of at least \$10^{-3}\$ relative or absolute, whichever is larger.

There will be at least one point and \$n\$ will be a positive integer.


Given input \$\{(0,0),(1,3),(4,2),(5,1)\}\$ and \$3\$ subdivisions:

For \$t=0\$, we just have \$(0,0)\$, and for \$t=1\$ we just have \$(5,1)\$.

For \$t=\frac13\$, we first go \$\frac13\$ of the way from each control point to the next to get \$\{(\frac13,1),(2,\frac83),(\frac{13}3,\frac53)\}\$. Repeating that once more gives us \$\{(\frac89,\frac{14}9),(\frac{25}9,\frac73)\}\$. Finally, if we do it once more, we get the single point \$(\frac{41}{27},\frac{49}{27})\$.

For \$t=\frac23\$, we first get \$\{(\frac23,2),(3,\frac73),(\frac{14}3,\frac43)\}\$, then \$\{(\frac{20}9,\frac{20}9),(\frac{37}9,\frac53)\}\$, and finally, \$(\frac{94}{27},\frac{50}{27})\$. And just for a sanity check, the points are indeed on the curve:

enter image description here

Note that these points do not evenly subdivide the Bezier curve by arclength. The arclength of a Bezier curve actually cannot be calculated exactly and subdividing like that would have to be done via approximations.

Test case generator

Credit to Wezl for the original idea.

  • \$\begingroup\$ love the interactive parts \$\endgroup\$ Dec 18 '21 at 17:28
  • \$\begingroup\$ When reading this I didn't expect it to be you having posted it lol \$\endgroup\$
    – emanresu A
    Dec 23 '21 at 7:55

Demonstrate some easier abstract algebra

From my related challenge, Demonstrate some advanced abstract algebra

Consider a binary operator \$*\$ that operates on a set \$S\$. For simplicity's sake, we'll assume that \$*\$ is closed, meaning that its inputs and outputs are always members of \$S\$.

Let's define some basic terms describing the properties of \$*\$. We can say that \$*\$ can have any of these properties, if they hold for all \$a,b,c \in S\$:

  • Commutative: \$a*b = b*a\$
  • Associative: \$(a*b)*c = a*(b*c)\$
  • Distributive: \$a*(b+c) = (a*b)+(a*c)\$, for some binary operator \$+\$ on \$S\$

We can also define 3 related properties, for a unary operation \$-\$ on \$S\$:

  • Anti-commutative: \$a*b = -(b*a)\$
  • Anti-associative: \$(a*b)*c = -(a*(b*c))\$
  • Anti-distributive: \$a*(b+c) = -((a*b)+(a*c))\$

Finally, we define 3 more, that only describe \$*\$ if the complete statement is true for \$a,b,c \in S\$:

  • Non-commutative: There exists \$a, b\$ such that \$a*b \ne b*a\$ and \$a*b \ne -(b*a)\$
  • Non-associative: There exists \$a, b, c\$ such that \$(a*b)*c \ne a*(b*c)\$ and \$(a*b)*c \neq -(a*(b*c))\$
  • Non-distributive: These exists \$a,b,c\$ such that \$a*(b+c) \ne (a*b)+(a*c)\$ and \$a*(b+c) \ne -((a*b)+(a*c))\$

We now have 9 distinct properties a binary operator can have: commutativity, non-commutativity, anti-commutativity, associativity, non-associativity, anti-associativity, distributivity, non-distributivity and anti-distributivity.

This does require two operators (\$-\$ and \$+\$) to be defined on \$S\$ as well. For this challenge we'll use standard integer negation and addition for these two, and will be using \$S = \mathbb Z\$.

Obviously, any given binary operator can only meet a maximum of 3 of these 9 properties, as it cannot be e.g. both non-associative and anti-associative.

Let's create a "table" of these properties:

Commutative Associative Distributive
Regular Commutative Associative Distributive
Anti Anti-commutative Anti-associative Anti-distributive
Non Non-Commutative Non-associative Non-distributive

Your task is to write 3 programs (either full programs or functions. You may "mix and match" if you wish).

Each of these 3 programs will:

  • take two integers, in any reasonable format and method

  • output one integer, in the same format as the input and in any reasonable method

  • be non-constant. That is, there exists at least two distinct inputs that have distinct outputs.

  • have exactly 3 of the 9 above properties. However, those three properties muse be in different rows and columns in the above table from each other. This means that it can be (for example) commutative, non-associative, anti-distributive; non-commutative, anti-associative, distributive; or anti-commutative, associative, non-distributive. But, it cannot be (for example) commutative, associative, distributive; non-commutative, non-associative, non-distributive; or non-commutative, anti-distributive, anti-associative.

This is ; the combined lengths of all 3 of your programs is your score, and you should aim to minimise this.

Additionally, you should include some form of proof that your programs do indeed have the required properties and do not satisfy the other properties. Answers without these are not considered valid.

Alternatively, a proof of impossibility is a valid answer. If you can demonstrate that there are no such programs that satisfy the criteria listed above, then this proof constitutes a valid answer as well.


  • \$\begingroup\$ There exists no anti-distributive surjection when \$S=\mathbb Z\$. Maybe there exists one when \$S=(\mathbb Z/2\mathbb Z)^k\$, but I haven't found one yet. \$\endgroup\$ Jun 16 '21 at 9:12
  • \$\begingroup\$ I would remove the constraint that the operator be a surjection, and just impose that it be non-constant. If you convince yourself that such an anti-distributive operator exists, you could post the challenge, but I would change it to "write 3-9 programs, such that each property is verified by (at least) one program". That would be an incentive to have programs which verify several properties at once, but make it more manageable. \$\endgroup\$ Jun 16 '21 at 9:18
  • \$\begingroup\$ Also, there are problems with your "anti-associativity": if b = 1, then (a*b)*c = a*(b*c). \$\endgroup\$
    – anatolyg
    Jun 16 '21 at 10:43
  • \$\begingroup\$ @RobinRyder If \$ S=(\mathbb Z / 2\mathbb Z)^k\$, aren't anti-distributive operators the same as distributive operators? \$\endgroup\$
    – Nitrodon
    Jun 16 '21 at 14:21
  • \$\begingroup\$ @Nitrodon Yes, of course you are right. \$\endgroup\$ Jun 16 '21 at 15:03

Twins' complements


Code Golf Birthday Cake

Your task is to print this exact text:

     0 2 4 6 8 10
     | | | | | |
    | Code Golf |
   | e---------f |
  | d___________l |
 | o-------------o |
| C_______________G |


  • Trailing or leading newline is allowed
  • , so shortest code wins!


  • Any feedback?
  • \$\begingroup\$ why is it lopsided \$\endgroup\$ Dec 21 '21 at 15:56
  • \$\begingroup\$ @thejonymyster fixed? \$\endgroup\$
    – Bgil Midol
    Dec 21 '21 at 15:57
  • \$\begingroup\$ No, that's more lopsided. You only need one $ between the Dennises, if that helps. \$\endgroup\$ Dec 21 '21 at 16:00
  • \$\begingroup\$ @thejonymyster fixed? \$\endgroup\$
    – Bgil Midol
    Dec 21 '21 at 16:18
  • \$\begingroup\$ Well now the bottom is asymmetric, but also what do the numbers mean? \$\endgroup\$ Dec 21 '21 at 17:16
  • \$\begingroup\$ @thejonymyster the site is about 9 years old \$\endgroup\$
    – Bgil Midol
    Dec 21 '21 at 18:27
  • 1
    \$\begingroup\$ Are you sure you want the bottom line have an extra # on left side but no such # on right side? \$\endgroup\$
    – tsh
    Dec 24 '21 at 5:30
  • \$\begingroup\$ @tsh fixed now? \$\endgroup\$
    – Bgil Midol
    Dec 24 '21 at 11:53
  • \$\begingroup\$ can you add more candles? \$\endgroup\$
    – Fmbalbuena
    Dec 27 '21 at 16:06

Order of an algebraic number

Consider some arbitrary polynomial with integer coefficients,

$$a_n x^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0 = 0$$

We'll assume that \$a_n \ne 0\$ and \$a_0 \ne 0\$. The solutions to this polynomial are algebraic numbers. For example, take the polynomial $$x^4 - 10x^2 + 1 = 0$$

We have that \$x = \sqrt 2 + \sqrt 3\$ is a solution to this polynomial, and so \$\sqrt 2 + \sqrt 3\$ must be an algebraic number. However, most real numbers, such as \$\pi\$ or \$e\$ are not algebraic.

Given any algebraic number \$x\$, it is possible to construct a polynomial \$p\$ such that \$p(x) = 0\$. However, this is not unique. For example, $$x^6 - 99x^2 + 10 = 0$$ also has a root \$x = \sqrt 2 + \sqrt 3\$. We define the minimal polynomial of an algebraic number \$x\$ to the be polynomial \$p\$ such that \$p(x) = 0\$ and the order of \$p\$ is minimal. With our example \$x = \sqrt 2 + \sqrt 3\$, there exists no such quadratic or cubic polynomial with \$x\$ as a root, as \$x^4 - 10x^2 + 1\$ is the minimal polynomial of \$x = \sqrt 2 + \sqrt 3\$. If the order of \$p\$ is \$n\$, we say that \$x\$ is an "algebraic number of order \$n\$". For example, \$\sqrt 2 + \sqrt 3\$ is of order \$4\$.

For the purposes of this challenge, we'll only consider real algebraic numbers termed "closed form algebraic numbers". These are algebraic numbers that can be expressed as some combination of addition, subtraction, multiplication, division and \$n\$th order radicals (for integer \$n\$).

For example, this includes \$\varphi = \frac {1 + \sqrt 5} 2\$, and \$7\sqrt[3] 2 - \sqrt[10] 3\$, but not e.g. roots of \$x^5 - x - 1 = 0\$, or \$\sqrt[\sqrt 2] 3\$ (\$n\$th roots are only allowed with integer \$n\$).

You are to take a real algebraic number as input, with the guarantee that it can be constructed with our 5 operations, and output the order of the input. The order will always be a positive integer.

You may take input in any form that exactly represents any closed form algebraic numbers. This could be as an exact symbolic number (if your language has these), a string unambiguously representing the composition of the 5 operations (e.g. 7*root(2,3)-root(3,10), 7*(2r3)-(3r10) or even sub(times(7, root(2, 3)), root(3, 10))), and so on. You may not input as floating point values. Note that the format you choose should be unambiguous, so is likely to use e.g. parentheses for grouping/precedence. For example, 7*2r3-3r10 does not meet this requirement, as it can be interpreted in a number of ways, depending on the precedence of each command.

In short, you may choose any input format - not limited to strings - so long as that input format can represent any closed form algebraic number exactly and unambiguously. Additionally, be mindful of this standard loophole about encoding extra information into the input format - this is fairly loose, but try not to use formats that contain more information than just the 5 standard operations.

If your answer uses a builtin that takes an algebraic number as input and returns either the order of the number, or the minimal polynomial, please edit it into this list of trivial answers.

This is , so the shortest code in bytes wins.

Test cases

I'm expressing the inputs here using Mathematica's Surd[n, k] function to represent \$\sqrt[k] n\$, along with +, -, * and / to represent \$+\$, \$-\$, \$\times\$ and \$\div\$ respectively.

input -> output
5/6 -> 1
Surd[4, 2] -> 1
Surd[2, 2] * Surd[2, 2] -> 1
(Surd[5, 2] + 1)*(Surd[5, 2] - 1) -> 1
(Surd[5, 2] + 1)/2 -> 2
(Surd[5, 2] + 1)*(Surd[5, 2] + 1) -> 2
Surd[2, 2] + Surd[3, 2] -> 4
Surd[(Surd[5, 2] + 1)/2, 2] -> 4
Surd[5, 5] - 2 -> 5
Surd[5, 5] + Surd[3, 7] - 2*Surd[2, 2] -> 70

The polynomials for these cases are given by Try it online!

  • \$\begingroup\$ i find it fascinating although its a bit beyond my knowledge of how to solve it \$\endgroup\$
    – don bright
    Dec 21 '21 at 7:41
  • \$\begingroup\$ Of course this is your challenge, and you can configure it as you wish. But I'd like to note that, by separating out any answers that employ Built-Ins into a Community Answer, you're effectively reducing this to a "Do X without Y" challenge, where "Y", in this case, is Built-Ins. That takes away the fun of being able to find just the right Built-In (or combination of two or three Built-Ins) to do the job... \$\endgroup\$
    – theorist
    Dec 24 '21 at 4:11
  • \$\begingroup\$ ...fun that you were happy to avail yourself of when you answered each of these two questions with a pair of Built-Ins: codegolf.stackexchange.com/questions/224125/… and codegolf.stackexchange.com/questions/229414/… \$\endgroup\$
    – theorist
    Dec 24 '21 at 4:12
  • \$\begingroup\$ Sorry I did not spot this problem when the challenge was still in sandbox: Surd in Mathematica only gives real roots. \$\endgroup\$
    – alephalpha
    Dec 24 '21 at 4:44
  • \$\begingroup\$ Deleted main post \$\endgroup\$ Dec 24 '21 at 16:25
  • 1
    \$\begingroup\$ @alephalpha I've edited the challenge to include the test cases suggested by you and tsh on the main post. I've also specified that the input will always be real \$\endgroup\$ Dec 24 '21 at 16:26
  • \$\begingroup\$ @theorist I already know that Mathematica essentially has a builtin for this - it wouldn't surprise me if other math-oriented langs (e.g. Pari/GP) also did. I'm not interested in solutions that off-hand all the work onto a builtin, but banning them isn't something I like doing. Therefore, I go by this suggestion to combine trivial builtin answers into a single CW answer. I'm well aware that I've posted builtin-only answers before, but only if the challenge doesn't combine trivial answers into a single CW answer (like I prefer to do) \$\endgroup\$ Dec 24 '21 at 16:31
  • \$\begingroup\$ There's three problems: (1) For all intents and purposes, the suggestion you are folowing does effectively ban builtins. By requiring any who answer to put builtin solutions into an anonymous community wiki, you are banning them from including builtins in their answers. The practice you've adoped just seems like a way to ban builtins in practice, while saying they're not "technically" banned. It's a "distinction without a difference." Thus I think those who adopt this practice shouldn't say "I'm not banning builtins".... \$\endgroup\$
    – theorist
    Dec 24 '21 at 22:08
  • \$\begingroup\$ Instead, I think it's more accurate to say: "I am banning builtins. But for those who want to post builtins anyways, you can put them into the Community Wiki." (2) Calling builtin answers "trivial", IMO, unfairly, well, trivializes the knowledge and understanding of a program needed to identify the right builtin for the job. Sure some can be trivial, but I don't think think they should be blanket-labeled as suchl. E.g., while you may have a different view, I don't think this was trivial: codegolf.stackexchange.com/questions/230836/leave-the-times-out/… ... \$\endgroup\$
    – theorist
    Dec 24 '21 at 22:10
  • \$\begingroup\$ The point of the linked example is that Defer wasn't designed to accomplish the goal set by the OP, but it nevertheless had that effect anyways. And you needed some understanding of how the language worked to realize it would do that. But it's still a simple one-word builtin. (3) Unless you're programming in machine code, all answers consist of a sequence of builtins. So it really comes down to an arbitrary cutoff of what's the minimum amount of builtins an answer needs to contain. \$\endgroup\$
    – theorist
    Dec 25 '21 at 0:03
  • \$\begingroup\$ To my understanding, the most complex thing here is not find out a minimal polynomial, but instead of how to simplify the input. Especially for testcases like \$\sqrt{\sqrt{5}+1}\cdot \sqrt{\sqrt{5}-1}\$, or \$\frac{5\sqrt{5}-1}{\sqrt{5}-1}\$. \$\endgroup\$
    – tsh
    Dec 27 '21 at 6:23

Domino tilings in an N-dimensional cube


Imagine an N-dimensional cube which has dimensions 2×2×...×2. Given the value of N (a positive integer), calculate the number of ways it can be divided into 2×1×1×...×1 "hyper-domino" pieces (two unit N-dimensional hypercubes glued together).

Standard rules apply. The shortest code in bytes wins.

Examples and test cases

For N = 1, the "cube" is a single domino. A single domino can be divided into a single domino in exactly one way, so the answer is 1.

For N = 2, the "cube" is a 2×2 square. It can be divided, or tiled, in two ways:

--  ||
--  ||

For N = 3, the cube is a 2×2×2 cube. It can be divided into four domino-cubes in nine different ways. One way to count it is to see that, if you pick a unit cube, it can be used by three different domino-cubes (one in each direction), and in all cases the rest forms a small staircase-like shape

L1  L2
#   #
##  ##

which can be divided into three pieces in three ways (# denotes a piece in Z-direction)

#   #
--  --

#   #
##  ##

|   |
|#  |#

which gives 3×3 = 9.

The corresponding sequence is A005271.

N    Answer
1    1
2    2
3    9
4    272
5    589185
6    16332454526976
7    391689748492473664721077609089

Number of complete rhyme schemes


Is it a perfect word?

  • \$\begingroup\$ @mathcat "The word may always be assumed to be lowercase." \$\endgroup\$ Jan 14 at 19:31

Number of arrangements of half a Rubik's cube

From a corner-on view of a Rubik's cube calculate the number of arrangements of stickers that are out of view.

Your input will provide the state of a Rubik's cube when viewed like the below image:

enter image description here

This input will be an array, in any defined order†, grouping†, and nesting† that you choose, containing the colours‡ of the \$27\$stickers (A.K.A. facelets or tiles) on three sides of a 3x3 Rubik's cube that join at one corner, like you can see above.

The input may be assumed to be that of a solvable state where only face turns can return the cube to having six sides with a single colour on each (if it isn't then your code may do anything, short of summoning Cthulhu).

† The input may be a flat list of colour-labels or you may specify that these labels will already be grouped in any way you wish (it may be a ragged, nested list for example), but the content thereof should only consist of the sticker colour-labels.

‡ Since the centres of the cube are actually fixed relative to each other, and hence the hidden centres' colours are known, you may choose to leave any or all of the central stickers out of the expected input (it could be as short as \$24\$ sticker colour-labels) while using a labeling that identifes the colours as the top-centre, left-centre, right-centre, and their three opposite colours. For the record, the standard colour theme, as in the image above, has orange opposite red, white opposite yellow, and green opposite blue (hence orange is the hidden centre sticker on the bottom etc.).

You should output the number of possible arrangements of sticker colours of the \$27\$ stickers which are not in the input (i.e. those stickers which are out of view). Note that swapping two of those stickers of the same colour is considered to be the same arrangement.

Sandbox questions

  1. Does this need test cases? (I'm not even 100% sure what the output should be if the input looked like a solved cube from that perspective although I may be able to work it out without writing a program it's certainly more than one - e.g. U' L R2 D' M D2 M' D' L' R2 U or R2 U R2 F2 R2 U2 F2 R2 F2 U R2)

  2. Is the spec clear?

  • \$\begingroup\$ You should probably make it more explicit that the center colors of the opposite faces are known. (Also, I'm fairly sure that a "solved cube" input would have an output of 192, but that's just me doing quick math in my head, so I could be wrong.) \$\endgroup\$
    – Nitrodon
    Jan 14 at 15:18

Solve nonimplication-SAT

  • \$\begingroup\$ I don't think there is really one set of "standard decision-problem rules" (as there are for sequence); you could just say something like "output using any two distinct values representing true and false" \$\endgroup\$
    – pxeger
    Dec 31 '21 at 23:26

Highlight a Wordle guess

In Wordle, you try to guess a secret word, and some letters in your guess are highlighted to give you hints.

If you guess a letter which matches the letter in the same position in the secret word, the letter will be highlighted green. For example, if the secret word is LEMON and you guess BEACH, then the E will be highlighted green.

If you guess a letter If you guess a letter which is present in the secret word, but not in the correct corresponding position, it will be highlighted yellow.

If a letter appears more times in the guess than it does in the secret word, only upto as many occur in the secret may be highlighted. If any of the occurrences are in the same place, they should be preferentially highlighted green, leaving earlier letters unhighlighted if necessary.

For example, with the secret LEMON and the guess SCOOP, the second O will be green, because it is in the right place, but the first O will be unhighlighted, because there is only one O in the secret, and one O has already been highlighted.

Any of the remaining letters in the secret may be highlighted yellow if they match, as long as the right number are highlighted in total. For example, with the secret LEMON and the guess GOOSE, only one of the Os should be highlighted; it does not matter which.


Given two five-letter strings, a secret and a guess, highlight the letters in the guess according to the rules above.

You can "highlight" the letters using any reasonable output format. For example:

  • a length-5 list of highlight values
  • a list of 5 pairs of (letter, highlight value)
  • a mapping from indices 0-4 or 1-5 to the highlight at that position

You can choose any three distinct values to represent unhighlighted, yellow, and green. (For example, 0/1/-1, or ""/"Y"/"G"...)

If in doubt about the "reasonable"ness of your output format, please ask. It must be unambiguous about the ordering of highlighting in case of double letters.


  • You may assume the inputs are both of length 5 and contain only ASCII letters
  • You may choose whether to accept input in uppercase or lowercase
  • You may use any standard I/O method
  • Standard loopholes are forbidden
  • This is , so the shortest code in bytes wins

Test cases \$ \require{color} \newcommand{\qG}[1]{\colorbox{##0f0}{$ \mathtt #1 $}} \newcommand{\qY}[1]{\colorbox{##ff0}{$ \mathtt #1 $}} \newcommand{\qW}[1]{\colorbox{ ##eee}{$ \mathtt #1 $}} \$

All using the secret word HELLO:

  • SCRAP -> \$ \qW S \qW C \qW R \qW A \qW P \$
  • HELLO -> \$ \qG H \qG E \qG L \qG L \qG O \$
  • EPOCH -> \$ \qY E \qW P \qY O \qW C \qY H \$
  • CIVIL -> \$ \qW C \qW I \qW V \qW I \qY L \$
  • BELCH -> \$ \qW B \qG E \qG L \qW C \qY H \$
  • ZOOMS -> \$ \qW Z \qY O \qW O \qW M \qW S \$ or \$ \qW Z \qW O \qY O \qW M \qW S \$
  • EERIE -> \$ \qW E \qG E \qW R \qW I \qW E \$
  • LILAC -> \$ \qY L \qW I \qG L \qW A \qW C \$
  • LLLLL -> \$ \qW L \qW L \qG L \qG L \qW L \$

Copy and paste friendly format


  • Is this clear enough?
  • Is this a duplicate?
  • Test-case suggestions?
  • Tag suggestions?
  • Any other feedback?
  • \$\begingroup\$ confused to be honest . maybeeee abit too hard? \$\endgroup\$
    – DialFrost
    Jan 17 at 9:57
  • \$\begingroup\$ @DialFrost Can you be more specific? What part are you confused about? \$\endgroup\$
    – pxeger
    Jan 17 at 9:58
  • \$\begingroup\$ er mostly about the highlighting value \$\endgroup\$
    – DialFrost
    Jan 17 at 10:00
  • \$\begingroup\$ @DialFrost do you mean: 1) you don't understand when to highlight the letters in which colour; or 2) you don't understand how the output values used for highlighting can be chosen? Or something else? \$\endgroup\$
    – pxeger
    Jan 17 at 10:01
  • \$\begingroup\$ both i dont understand \$\endgroup\$
    – DialFrost
    Jan 17 at 10:01
  • \$\begingroup\$ @DialFrost without some more details on what you're missing, I can't help you to understand or clarify the description. What bits you do you understand? \$\endgroup\$
    – pxeger
    Jan 17 at 10:05
  • \$\begingroup\$ pretty much none i just meant i dont understand the hilighting value and how it works the most \$\endgroup\$
    – DialFrost
    Jan 17 at 10:06

Is this continuous terrain?

  • \$\begingroup\$ [Suggested Testcase](Try it online!) \$\endgroup\$
    – Fmbalbuena
    Jan 10 at 0:23
  • \$\begingroup\$ I am unsure if you should allow both ~ and -. Can one even freely mix them? \$\endgroup\$ Jan 10 at 12:33
  • \$\begingroup\$ @JonathanFrech as in you can choose to take input with overlines replaced with one of them \$\endgroup\$
    – emanresu A
    Jan 11 at 8:39
  • \$\begingroup\$ question name idea: "is this continuous terrain?" I have a feeling there is a dupe of this. \$\endgroup\$
    – Razetime
    Jan 14 at 4:05
  • \$\begingroup\$ @Razetime Good idea! \$\endgroup\$
    – emanresu A
    Jan 14 at 8:25

Climb a ragged list

Your task is to represent a ragged list as ASCII art that looks like a mountain.
You are given a list of lists, either having other lists inside them or being empty.

Here is somewhat a description:

Looping through every list:
    If entering a list, print (current_depth - max_depth - 1) newlines with a "/"
    If exiting a list, print (current_depth - max_depth - 1) newlines with a "\"

The printing in the description is from left to right, top to bottom.
So [[[[]], [[]]]] would output (max depth = 3):

  /\  /\
 /  \/  \
/        \


Test Cases:

In: [] # empty list

In: [[]]

In: [[], [[]], [[[]]]]
   /\  /  \
/\/  \/    \

In: [[[[]], []]]
 /  \/\
/      \

In: [[], [[]], [[], []], [[[]], []]]
   /\  /\/\  /  \/\
/\/  \/    \/      \

In: [[[[], []], [[]]], [[[]], [[], [[], [], []]]], [[[], [], []]]]
  /\/\  /\    /\  /\/      \    /\/\/\
 /    \/  \  /  \/          \  /      \
/          \/                \/        \

Good Luck!

Example Python script with a different approach

  • \$\begingroup\$ Seems like a dupe of this treating the array as a string... \$\endgroup\$
    – emanresu A
    Jan 17 at 2:21

Sides of a polygon

  • \$\begingroup\$ Will the shape touch itself? Say, like this or this ? \$\endgroup\$
    – tsh
    Dec 27 '21 at 5:40
  • \$\begingroup\$ @tsh No,it won't. \$\endgroup\$
    – emanresu A
    Dec 27 '21 at 5:56
  • \$\begingroup\$ By your current examples, this is a valid shape although it looks very strange. \$\endgroup\$
    – tsh
    Dec 29 '21 at 7:15
  • \$\begingroup\$ @tsh Yeah, I’ll just leave that since allowing those shapes doesn’t car assist any problems or ambiguousities. \$\endgroup\$
    – emanresu A
    Dec 29 '21 at 8:18
  • \$\begingroup\$ I would like for the valid inputs to be more clearly defined. How many sides does @ths's "very strange" looking shape have? \$\endgroup\$ Jan 10 at 12:52

BCD to binary, with bitwise

In this challenge, you'll convert an 8-digit BCD (Binary Coded Decimal) number to a 32 bit (unsigned) integer in the fewest instructions possible, with only bitwise instructions available.


You'll be given a single positive integer as input, from 00000000 to 999999999. It will be represented using BCD, as a 4-byte unsigned integer, with each nibble being a decimal digit from 0000 (0) to 1010 (10). More significant nibbles will correspond to more significant digits of the decimal number.

Your output should be that same number, as an ordinary 32-bit integer.


This is atomic code golf, so you can only use the following instructions, the number of which is used for scoring:

and [r], [r|I]      Bitwise AND
or  [r], [r|I]      Bitwise OR
xor [r], [r|I]      Bitwise XOR

not [r]             Bitwise NOT

shr [r], [r|I]      Shift right (zero fill)
shl [r], [r|I]      Shift left

mov [r], [r|I]      Copy

All instructions will write their output to the first register listed, and for the second argument [r|I] indicates either a register or an immediate (any 32-bit constant) can be provided.

You have four registers to work with, all of which hold a single 4 byte unsigned integer: ra, rb, rc, and rd. Any instruction using only registers costs 1 byte, and any with an immediate cost a total of 4 (this isn't technically possible, since the immediates are 4 bytes on their own, but I don't want to make them too costly).

Input will be provided in ra, and the contents of ra when your program is finished will be used as output. All other registers will be initialized to 0.

Instructions Mk. 2:

This is atomic code golf, so you can only use the following instructions, the number of which is used for scoring:

and [r], [r|I]      Bitwise AND
or  [r], [r|I]      Bitwise OR
xor [r], [r|I]      Bitwise XOR

not [r]             Bitwise NOT

shr [r], [r|I]      Shift right (zero fill)
shl [r], [r|I]      Shift left

mov [r], [r|I]      Copy

goto [r|I]          Go to an instruction (`0` is the start of the program)
goif [r] [r|I]      Go to an instruction, if `r` is not all `0`s

All instructions (aside from goto and goif) will write their output to the first register listed, and for the second argument [r|I] indicates either a register or an immediate (any 32-bit constant) can be provided.

You have 8 registers to work with, all of which hold a single 4 byte unsigned integer: ra, rb, rc, rd, rk, rn, rp, and rs. Any instruction using only registers costs 1 score, and any with an immediate cost a total of 2.

Input will be provided in ra, and the contents of ra when your program is finished will be used as output. All other registers will be initialized to 0.


I don't actually know if this is an interesting challenge, or if more registers will be needed, or if there's already a well known solution. I'd try it myself but it's kinda late here so I'm too tired to, and if I don't post this now I'll forget about it lol

  • \$\begingroup\$ Maybe just give infinite amount of registers and don't call them "byte" but "score"? \$\endgroup\$
    – l4m2
    Jan 18 at 12:29

Compress and decompress

  • \$\begingroup\$ self-referential might be better than quine. But are you assuming normal quine rules? Are programs allowed to introspect their own source code? \$\endgroup\$
    – pxeger
    Jan 17 at 10:15
  • \$\begingroup\$ This challenge is fairly similar to Encode a Lenguage, but I think it's sufficiently open-ended that it's different in an interesting way. \$\endgroup\$
    – pxeger
    Jan 17 at 10:18
  • \$\begingroup\$ Personally I think this would be more interesting if you were allowed to read your source code, because otherwise it becomes too much of a quine variant where most of the code is taken up by encoding the program's source code, and not the interesting task (which is the compression). (Sorry, I probably should have given you this opinion before I asked you to decide whether quine rules applied) \$\endgroup\$
    – pxeger
    Jan 17 at 10:26
  • 1
    \$\begingroup\$ @pxeger I added the quine rules specifically to discourage solutions where you just swap your programs source code and a single input. The other (more interesting imo.) approach is to actually do compression and then make your source code compressible. \$\endgroup\$
    – AnttiP
    Jan 17 at 10:32

Crack the Caesar cipher

The Caesar cipher is a simple and famous cipher, where the letters of the alphabet are rotated by some secret amount. For example, if our secret rotation is 3, we would replace a with d, b with e, w with z, x with a and so on.

Here is an example (rotation amount: 10):

Robo sc kx ohkwzvo

This cipher is very weak, because short common English words like "I", "a", "is", "an", "if", etc. are easy to detect. Your task is to crack a Caesar cipher, that is, recover the rotation amount from the ciphertext. As additional input, you are given a list (or set) of words, which the plaintext can contain. It is guaranteed that there is only one answer.


"Ifmmp Xpsme!", ["world", "banana", "hello"]
-> 1

"Nc cd, Kadcn?", ["cogito", "et", "ergo", "tu", "sum", "brute"]
-> 9

"boring", ["boring"]
-> 0

IO rules

The ciphertext can contain any printable ascii characters. The dictionary (list of words) contains strings made of lowercase letters (a-z). Only letters are rotated (punctuation is ignored). You will output an integer in the range [0,25]

  • \$\begingroup\$ Can we not have to deal with capitalisation? \$\endgroup\$
    – emanresu A
    2 days ago

Prime Number Fibonacci

In this challenge, you will make a program that calculates the Fibonacci sequence with a twist. Instead of it starting with 0 and 1, it starts with the nth prime number determined by input by the user. The second number is the nth+1 prime number. The sequence should also stop after nth number iterations.


  1. Get a number from the input. We will call it n
  2. Calculate the n prime number and n+1 prime number
  3. Make a function that adds these numbers and calls itself with the result.
  4. Make the function stop once prime number with index n numbers are output





By the way, here is the JavaScript code I used for this example:

var primeNumber1 = prime(num);
var primeNumber2 = prime(num+1);
function fib(num1,num2,iterations,max){
if(iterations == max+1){
function prime(number){
var numPrime = 0;
for(var i = 0; i > -1; i++){
if(numPrime == number){
return i;
function isPrime(num) {
  for(var i = 2; i < num; i++)
    if(num % i === 0) return false;
  return num > 1;
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  • \$\begingroup\$ I would define the task more clearly. Something along the lines of (if I understood correctly) "Let \$(p_k)_{k\geq 1}\$ denote the ordered sequence of all prime numbers. Given a natural number \$n\geq 1\$, output \$(a_1,\dots,a_{p_n+p_{n+1}})\$ where \$a_{-1}:=p_n\$, \$a_0:=p_{n+1}\$ and \$a_k:=a_{k-2}+a_{k-1}\$ for \$k\geq 1\$." \$\endgroup\$ 2 days ago
  • \$\begingroup\$ @JonathanFrech I have no idea what those symbols mean except for greater than and I know := is used in statically typed programming language to infer the type of a variable. Could you explain what the math string means and how it would clarify my question? \$\endgroup\$ 2 days ago
  • \$\begingroup\$ When you say "the nth prime number", is for you 2 the prime number with index \$0\$ or \$1\$? I guess the latter, so \$p_1=2\$. Then I understand your task to be printing \$p_n\$ integers which are defined as follows: the first number to be printed is \$a_1=p_n+p_{n+1}\$, the second is \$a_2=p_{n+1}+a_1\$, the third \$a_3=a_1+a_2\$ and so on up to \$a_{p_n+p_{n+1}}\$. I found it hard to read into your explanation and would like a more clear definition of the task -- be it with formulae or word descriptions. \$\endgroup\$ yesterday
  • \$\begingroup\$ I guess my problem is that I have to infer from your example that the 2nd prime number is 3 and "Make a function that adds these numbers and calls itself with the result." requires thinking of Fibonacci to properly interpret. \$\endgroup\$ yesterday

Mat Printing Matrix

  • \$\begingroup\$ er wats default I/O @adam \$\endgroup\$
    – DialFrost
    Jan 17 at 11:56
  • \$\begingroup\$ im sorry i dont understand @adam could u explain the defualt IO (i alr read the link doesnt rly help) or edit my post thx \$\endgroup\$
    – DialFrost
    Jan 17 at 12:02
  • \$\begingroup\$ like this? i changed it \$\endgroup\$
    – DialFrost
    Jan 17 at 12:08
  • \$\begingroup\$ Yeah, this looks great. Maybe put in the tags you plan on using. \$\endgroup\$
    – Adám
    Jan 17 at 12:55
  • \$\begingroup\$ @adam pls edit the tags if its wrong thx \$\endgroup\$
    – DialFrost
    Jan 17 at 13:24

Implement an argwhere function


  • \$\begingroup\$ Interesting. I'm guessing "no", but are langs without function definition allowed to participate? \$\endgroup\$ Jan 14 at 19:53
  • \$\begingroup\$ @thejonymyster I'm not too interested in making restrictions. If your language can accept code as input and run it to make decisions, I'd say that's good enough. But as with all functional-programming questions, some languages will inevitably be excluded. \$\endgroup\$
    – chunes
    Jan 15 at 5:47

Move to Right and left


Your task is to Move Right and left. If the numbers combine, sum.


A simple example is [1] gives [1, 0, 1] because

  / \
 /   \
[1, 0, 1]

Another example

   [1, 2]
   /\ /\
  /  X  \
[1, 2, 1, 2]

Another example

   [1, 2, 3]
   /\ /\ /\
  /  X  X  \
[1, 2,\/ \  \
       4, 2, 3]

Test cases

[1,2,3] => [1,2,4,2,3]
[4,2] => [4,2,4,2]
[1] => [1,0,1]
[7,4,5,6] => [7,4,12,10,5,6]
[1,2,4,2,1] => [1,2,5,4,5,2,1]
[1,0,1] => [1,0,2,0,1]
[1,0,2,0,1] => [1,0,3,0,3,0,1]
[8,7,6,5,4] => [8,7,14,12,10,5,4]
[1,4,9,16] => [1,4,10,20,9,16]
[1,2] => [1,2,1,2]
  • \$\begingroup\$ why are there X crossings? wouldn't they just combine right there? \$\endgroup\$ yesterday
  • \$\begingroup\$ @thejonymyster this is cross. \$\endgroup\$
    – Fmbalbuena
31 32
34 35

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