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Decorate Pascal's Triangle

Although what is a Pascal's triangle is well-known and we already can generate it, the task is now different: Output $n$ first lines of the Pascal's triangle as colored bricks. Color number is ...
1k views

Permutations in Disguise

Given a $n$-dimensional vector $v$ with real entries, find a closest permutation $p$ of $(1,2,...,n)$ with respect to the $l_1$-distance. Details If it is more convenient, you can use ...
215 views

Multiplication in the Steenrod Algebra

Here's yet another Steenrod algebra question. Summary of the algorithm: I have a procedure that replaces a list of positive integers with a list of lists of positive integers. You need to repeatedly ...
1k views

Generate basis elements of the Steenrod algebra

The Steenrod algebra is an important algebra that comes up in algebraic topology. The Steenrod algebra is generated by operators called "Steenrod squares," one exists for each positive integer i. ...
5k views

Amount of permutations on an NxNxN Rubik's Cube

Introduction: A 3x3x3 Rubik's Cube has $43,252,003,274,489,856,000$ possible permutations, which is approximately 43 quintillion. You may have heard about this number before, but how is it actually ...
310 views

Generate the k-ary necklaces of length n

The set of necklaces is the set of strings, where two strings are considered to be the same necklace if you can rotate one into the other. Your program will take nonnegative integers ...
481 views

Fastest algorithm to output array containing all integers in range excluding duplicate digits

Input is a single integer in ascending digit order. The only valid inputs are: 12 123 1234 ...
2k views

Cartesian product of a list with itself n times

When given a a list of values and a positive integer n, your code should output the cartesian product of the list with itself n ...
2k views

Sign-Swapping Sums

Given a nonempty list of positive integers $(x, y, z, \dots)$, your job is to determine the number of unique values of $\pm x \pm y \pm z \pm \dots$ For example, consider the list $(1, 2, 2)$. ...
325 views

Permutations such that no k+2 points fall on any polynomial of degree k

Description Let a permutation of the integers {1, 2, ..., n} be called minimally interpolable if no set of k+2 points (together ...
230 views

Compute number of matrices with appropriate sums

When multiplying monomials in the Milnor basis for the Steenrod algebra, part of the algorithm involves enumerating certain "allowable matrices". Given two lists of nonnegative integers r1, ... ,rm ...
882 views

Mod 2 Multinomial coefficients

quintopia has posted here a challenge to compute multinomial coefficients (some of the text here is copied from there). There is a fun algorithm to compute multinomial coefficients mod 2. Given a ...
510 views

Determine How many Wheels There Are

Non-math explanation This is an explanation that is meant to be approachable regardless of your background. It does unfortunately involve some math, but should be understandable to most people with a ...
194 views

Those annoying grasshoppers [closed]

The problem #6 of IMO 2009 reads: Let a 1, a 2, a 3, ..., a n, be distinct positive integers and let T be a set of n-1positive integers not containing a 1+a 2+a 3+...+a n, A grasshopper is to ...
364 views

Distinct Reversible Primitive Binary Necklaces

Introduction - What is a necklace? A necklace is something that OEIS people are obsessed with. The OEIS challenge has like 5 necklace sequences. A binary necklace of length ...
2k views

How many partitions do I have?

The partition number of a positive integer is defined as the number of ways it can be expressed as a sum of positive integers. In other words, the number of integer partitions it has. For example, the ...
1k views

How many partitions contain only perfect squares?

Given a non-negative integer or a list of digits, determine in how many ways can the number be formed by concatenating square numbers, which may have leading zeroes. Examples ...
1k views

Finding approximate correlations

Consider a binary string S of length n. Indexing from 1, we can compute the Hamming ...
586 views

Maximal discrepancy-2 sequence with minimal entropy

Background As noted in the PPCG challenge Compress a maximal discrepancy-2 sequence – which inspired this challenge – the authors of the paper Computer-Aided Proof of Erdős Discrepancy Properties ...
348 views

Stable marriage problem

Background Suppose that there are 2*n people to be married, and suppose further that each person is attracted to exactly n ...
2k views

Necklace splitting problem

Background I was inspired by 3Blue1Brown's recent video about the necklace splitting problem (or as he calls it, the stolen necklace problem) and its relationship to the Borsuk-Ulam theorem. In this ...
3k views

Absolute Sums of Sidi Polynomial Coefficients

Background The Sidi polynomial of degree n – or the (n + 1)th Sidi polynomial – is defined as follows. The Sidi polynomials have several interesting properties, but so do their coefficients. The ...
409 views

Evaluate the Binomial Coefficient [duplicate]

Given two nonnegative integers n,k such that 0 <= k <= n, return the binomial coefficient ...
6k views

A penny saved is a penny

...counted! You will pass your program a variable which represents a quantity of money in dollars and/or cents and an array of coin values. Your challenge is to output the number of possible ...
2k views

Compute the Eulerian number

The Eulerian number A(n, m) is the number of permutations of [1, 2, ..., n] in which exactly ...
2k views

Figure Out the Android Lock Pattern

Lets say you saw your friend enter his or her password into their Android phone. You don't remember how they made the pattern but you remember what the pattern looks like. Being the concerned friend ...
339 views

Verify a ballot triangle

A ballot number, which we'll label B, is the number of ways of arranging the numbers from 1 through B(B+1)/2 into a triangle, such that each row and column is in any increasing order. The first four ...
2k views

Number of cycles of a permutation

Consider a permutation of the integers 1, ..., n, such as this one for n = 6: ...
823 views

Is case sensitivity important? Part II: reality check

In this question Tom learned that, in general, there are many motivations to choose to include case sensitivity in his programming language, because the possible combinations for a variable name are ...
2k views

Is case sensitivity important?

Tom is going to implement a new programming language of his invention. But before actually starting working on it, he wants to know whether his language should be case sensitive or not. On one hand, ...
1k views

Calculate the partitions of N

Your challenge is simple: GIven an integer N, ouput every list of positive integers that sums to N. For example, if the input was 5, you should output ...
4k views

The handshake problem

The handshake problem is the classic problem that for n people in a room, if they all shake hands, what's the total number of handshakes that occur. You code should take an input of any number and ...
3k views

Has My Pie Been Bisected?

Write a program or function that takes in a nonempty list of positive integers. You may assume it is input in a reasonable convenient format such as "1 2 3 4" or <...
819 views

Permutations with Indistinguishable Items

Given a list of integers, output the number of permutations of the integers, with indistinguishable permutations counted once. If there are n integers, and each ...
416 views

Same-color arithmetic progressions

Van der Waerden's theorem says that For any given positive integers r and k, there is some number ...
2k views

Compute the multinomial coefficient

Time for another easy challenge in which all can participate! The multinomial theorem states: The expression in parentheses is the multinomial coefficient, defined as: Allowing the terms ki to ...
5k views

Bernoulli Numbers

The Bernoulli numbers (specifically, the second Bernoulli numbers) are defined by the following recursive definition: Where denotes a combination. Given a nonnegative integer ...
3k views

Count sums of two squares

Given a non-negative number n, output the number of ways to express n as the sum of two squares of integers ...
297 views

Rearrangement Inequality

Background The Rearrangement Inequality is an inequality that is based on rearranging numbers. If I have two lists of numbers of the same length, x0, x1, x2...xn-1 and y0, y1, y2...yn-1 of the same ...
329 views

Enumerating N-Dimensional Vectors

Given a positive integer k > 1 and a non-negative integer i, generate a k-tuple (or ...
149 views

Generate ordered binary combinations without repetitions [closed]

Challenge Write the shortest program that receives two signed integers n and i and for each ...
1k views

Hook length product

A Young diagram is an arrangement of boxes in left-justified rows and top-justified columns. For each box, all the spaces above it and to its left are occupied. ...
614 views

Supersonic domino tilings

Task Write a program that reads three integers m, n either from STDIN or as command-line arguments, prints all possible tilings of a rectangle of dimensions m × n by 2 × 1 and 1 × 2 dominos and ...
350 views

Plus one sheep minus one sheep [closed]

Once upon a time long long ago... when there was no money or stocks yet, people were trading sheep. Even before (but close to) the invention of abacus, the great-grandfather of Warren Buffet decided ...
975 views

Matrix property X revisited (or the Joy of X)

This challenge is partly an algorithms challenge, partly an optimization challenge and partly simply a fastest code challenge. A T matrix is fully specified by its first row ...
627 views

Count the number of Hankelable matrices

Background A binary Hankel matrix is a matrix with constant skew-diagonals (positive sloping diagonals) containing only 0s and 1...
1k views

Combinatorial products of unique primes

Statement of problem Given a set of unique, consecutive primes (not necessarily including 2), generate the products of all combinations of first powers of these primes — e.g., no repeats — and also 1....
2k views

Fibonacci domino tiling

There's classic combinatorial result that the number of ways to tile a 2*n strip by 1*2 dominoes is the nth Fibonacci number. ...