Questions tagged [combinatorics]
A puzzle based on combinatorics, which is the study of counting discrete structures. Use with [mathematics]
899 questions
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"Interlacing" the 8 Queens Problem
Let "attacking" mean protecting, but everyone says "attacking"...
Let Q be a chess position with q non-attacking queens, R one with r rooks, B b bishops, N n knights and P p pawns (...
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That's a lot of triangles
Counting the triangles in this image individually would take far too long. What is a human (not computer) algorithm to figure out how many triangles are in this shape? Answers should include the ...
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Vote for the election
At a recently held election one party fielded 3 candidates A,B and C. In this election people can vote for any number of candidates in a desired party. The voting pattern of 100 people as follows: The ...
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Flip a Fair Coin
I found this question and became curious, can anyone tell me the answer and prove it, i know it seems fairly simple but just thought an explanation of this would make an interesting case.
Flip a fair ...
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Relabeling two 20-sided dice without changing their total
Usually, 20-sided dice are labeled with the numbers 1 to 20. When you roll two of these, their sum is a random number between 2 and 40. The total 21 is most likely to occur, while 2 and 40 are the ...
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Alice splits the bill not too generously with Bob
Alice and Bob go out for dinner and the restaurant bill is 100€. Beforehand, they had agreed to evenly pay half of the bill, but suddenly Alice is in a bit of a generous mood and offers Bob a ...
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How many trails from A to C?
Consider the following graph (3 edges between A,B; 3 edges between B,C; 2 edges between A,C).
How many trails are there that start from vertex A and end at vertex C? Two trails are considered the same ...
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A tree-cutting problem [closed]
Dans un parc il y a 10000
arbres (vus comme des points), placés en un quadrillage carré de 100
lignes et 100
colonnes. Déterminer le nombre maximal d'arbres que l'on peut abattre de sorte que, quelle ...
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The question contains the answer (literally)
How many ways to choose 3 letters from ONE? Answer: 1
How many ways to choose 1 letter from FOUR? Answer: 4
How many ways to choose 2 letters from SEVEN? Answer: 7
What is the largest n such ...
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Pairing 6 badminton players into singles games
Six people go to play badminton on three singles courts. There are ten ways to divide them into two teams. For each division into two teams, there are six ways to pair off players from one team ...
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From honeycombs to a cube
Can you prove the following identity with minimal calculation?
The sum on the left hand side has n increasing honeycombs and we are counting hexagons in all the honeycombs.
Source: Inspired by a ...
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Which station is my Uncle's restaurant? - Where's Wally? remix in Paris Subway
Finding my uncle's restaurant station on the Parisian RATP subway is a little like "Where's Wally?"
You are given the next Paris' subway map. Please click on it or here to obtain a zoomed ...
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Beetles on a Chessboard
This question is taken from Problem-Solving Strategies by Arthur Engel.
The question says:
A beetle sits on each square of a 9 x 9 chessboard. At a signal each beetle crawls diagonally onto a ...
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Another “divide the candies” puzzle
I have asked two questions, here and here, with this theme before. Here’s another one.
My sister and her family were visiting us over the summer. Before they left, I bought a bag of candies for her ...
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Covering an 8x8 grid with X pentominoes
What is the minimum number of X pentominoes you need to cover every cell of an 8x8 grid? Pentominoes may overlap each other and sit outside the boundary of the grid. An X pentomino looks like this:
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