Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [combinatorics]

For challenges involving combinatorics.

-3
votes
0answers
144 views

Permutations to the nines redux [on hold]

Note: This question has been challenging to describe; full disclosure How to make question clear to users who voted to close without providing feedback as to what is not clear to them?; OEIS A217626: ...
4
votes
2answers
224 views

Find arrays with distinct subarray sums

Consider an array A of length n. The array contains only integers in the range 1 to ...
5
votes
1answer
375 views
+50

Count arrays that are really unique

This is a follow up to Count arrays that make unique sets . The significant difference is the definition of uniqueness. Consider an array A of length ...
0
votes
3answers
360 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 ...
6
votes
4answers
153 views

Seeking Substantial Subcollections

(thanks to @JonathanFrech for the title) Challenge Write a program or function that, given a collection of positive integers \$S\$ and a positive integer \$n\$, finds as many non-overlapping ...
11
votes
3answers
424 views

Count arrays that make unique sets

This question has a similar set up to Find an array that fits a set of sums although is quite different in its goals. Consider an array A of length ...
9
votes
12answers
1k views

Different combinations possible

Problem Given a value n, imagine a mountain landscape inscribed in a reference (0, 0) to (2n, 0). There musn't be white spaces between slopes and also the mountain musn't descend below the x axis. ...
11
votes
2answers
265 views

Removing points from a triangular array without losing triangles

I have a combinatorics problem that I'd like to put on the OEIS—the problem is that I don't have enough terms. This code challenge is to help me compute more terms, and the winner will be the user ...
19
votes
12answers
2k views

Socket - Plug compatibility

Traveling with electronics is always fun, especially when you need an adapter to charge them. Your challenge is to make planning a trip a little easier by checking if a given plug will be compatible ...
27
votes
4answers
712 views

Smallest region of the plane that contains all free n-ominoes

On Math Stack Exchange, I asked a question about the smallest region that can contain all free n-ominos. I'd like to add this sequence to the On-Line Encyclopedia of Integer Sequences once I have ...
13
votes
12answers
1k views

Fun with strings and numbers

Here's a programming puzzle for you: Given a list of pairs of strings and corresponding numbers, for example, [[A,37],[B,27],[C,21],[D,11],[E,10],[F,9],[G,3],[H,2]]...
16
votes
27answers
3k views

The Unique Padlock PIN List!

Introduction In a private chat, a friend of mine apparently recently stumbled across a security system which has the following two restrictions on its valid pins: Each digit must be unique (that is "...
10
votes
22answers
1k 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 ...
24
votes
34answers
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)\$. ...
8
votes
4answers
495 views

Count the number of ways of putting balls into bins

In this task you are given an odd number of white balls and the same number of black balls. The task is to count all the ways of putting the balls into bins so that in each bin there is an odd number ...
14
votes
1answer
288 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 with their indices) fall on a polynomial of degree k. That is, No ...
3
votes
2answers
74 views

Count stacking sequences [duplicate]

Given a list of stack heights, calculate the number of ways those heights could have been arrived at by stacking blocks one at a time. Shortest code wins. Test cases: ...
16
votes
1answer
286 views

Counting polystrips

Polystrips are a subset of polyominoes conforming to the following rules: each piece consist of 1 or more cells no cell can have more than two neighbours the cells should not enclose a hole Free ...
8
votes
17answers
775 views

Sum of combinations with repetition

Write the shortest code you can solving the following problem: Input: An integer X with 2 <= X and X <= 100 Output: ...
17
votes
8answers
769 views

Conjugate permutations

A permutation of size n is a reordering of the first n positive integers. (meaning each integer appears once and exactly once). Permutations can be treated like functions that change the order of a ...
14
votes
8answers
435 views

Deranged Rearrangements

Your task is to write a computer program such that when it is cut up into lines (split on the newline character) every arrangement of the lines will output a different number between 1 and n! (where n ...
8
votes
6answers
416 views

Alice's Tea Party

There are n places set around a circular table. Alice is sat on one of them. At each place, there's a cake. Alice eats her cake, but it doesn't taste very nice. Then the Mad Hatter comes in. He gives ...
23
votes
26answers
2k views

Find The Rank Of A Word

Definition The rank of a word is defined as the position of the word when all the possible permutations (or arrangements) of its letters are arranged alphabetically, like in a dictionary, no matter ...
12
votes
4answers
226 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 ...
14
votes
16answers
858 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 ...
13
votes
5answers
305 views

Integer triangles with perimeter less than n

Definition An "integer triangle" is one with integer coordinates. For example the following triangle is an integer triangle: ...
21
votes
3answers
721 views

​L​o​o​p​ ​I​t​

Note: The title of this question should be "Loop It", but because title needs to be at least 15 characters, there are some invisible spaces. This note is such that the challenge can be searched for. ...
19
votes
13answers
2k views

Is it a shuffle?

Yesterday I asked this question about riffle shuffles. It seems that yesterdays question was a bit too hard so this question is a related but much easier task. Today you are asked to determine if a ...
19
votes
23answers
2k views

Single swaps of an array

Inspired by Taken from a question at Stack Overflow. The challenge Given an integer n>1, output all arrays that can be obtained by swapping exactly two entries ...
18
votes
2answers
450 views

How many shuffles

A riffle shuffle is a type of shuffle where the deck is split into two partitions and the partitions are then spliced back together to create a new shuffled deck. The cards are spliced together in ...
7
votes
4answers
200 views

Prefixless Palindromes

Write a program or function that takes N, and S and outputs the number of palindromes of length S you can build using an alphabet of size N such that any prefix of size between 2 and S-1 is not a ...
9
votes
4answers
259 views

Now we're thinking in n dimensions!

The question: Given an a number n ≥ 2, how many distinct pairs of points on an n-dimensional ...
16
votes
9answers
639 views

XKCD Calendar Facts

Inspiration. Posted with permission. Print one of the possible XKCD calendar "facts": You can get the raw text and structure from my APL reference implementation or from Explain XKCD's transcript (...
17
votes
10answers
2k views

Enumerate all possible grids of integers with constraints

Problem Consider a square 3 by 3 grid of non-negative integers. For each row i the sum of the integers is set to be r_i. ...
19
votes
9answers
729 views

Hand patterns in a card game

A deck of cards is the Cartesian product of S suits and R ranks. Many, though not all, card games use ...
5
votes
1answer
243 views

Bobby's Booby-Trapped Safe

Bobby's booby-trapped safe requires an n-digit code to unlock it. Alex has a probe which can test combinations without typing them onto the safe. The probe responds Fail if no individual digit is the ...
20
votes
8answers
860 views

Pick-flatten a list

Consider the process of "picking" a nested list. Picking is defined as follows: If the argument is a list, take an element from the list at random (uniformly), and pick from that. If the argument is ...
13
votes
10answers
540 views

Counting Fibonacci Orbits

If we define a Fibonacci-like sequence as fk(n) = (fk(n-1) + fk(n-2)) % k, for some integer k (where % is the modulo operator), the sequence will necessarily be cyclic, because there are only k2 ...
23
votes
5answers
503 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 ...
19
votes
7answers
878 views

Number of distinct non-empty subsequences of binary expansion

A subsequence is any sequence that you can get from another by deleting any amount of characters. The distinct non-empty subsequences of 100 are ...
4
votes
0answers
193 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 ...
7
votes
6answers
357 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 ...
15
votes
16answers
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 ...
9
votes
16answers
642 views

Restricted Integer Partitions

Pk(n) means the amount of partitions of n into exactly k parts. Given n and ...
11
votes
3answers
794 views

How many ways can a road cross a river?

Imagine a straight river and a road that goes across the river n times through bridges. The road does not loop on itself and is infinitely long. This road would be considered an open meander. An open ...
16
votes
7answers
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 ...
9
votes
4answers
377 views

Maximum number of distinct substrings

Description Given a length n, and an alphabet size k>0, your program must determine the number of strings with those ...
15
votes
6answers
1k views

BASKETBALL FRVR?

You might already be familiar with the game: Basketball FRVR in facebook. There are two types of score you can make: A virgin-shot:(we call it so in our country :D) When the ball enters the basket ...
11
votes
3answers
322 views

Lyndon word factorization

Background A Lyndon word is a non-empty string which is strictly lexicographically smaller than all its other rotations. It is possible to factor any string uniquely as the concatenation of Lyndon ...
11
votes
27answers
768 views

All non-ordered pairs between the elements of an array

Task: Return an array with all possible pairs between the elements of an array. Example From a=["a", "b", "c", "d"]; return ...