Questions tagged [combinatorics]
A puzzle based on combinatorics, which is the study of counting discrete structures. Use with [mathematics]
901 questions
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Prove/disprove that polygons on a sheet of paper having a common edge, can always be colored with one of two different colors.
Several straight lines drawn on a sheet of paper divide it into polygons. Is it always possible to color each polygon with one of two colors so that any two polygons that share an edge are of ...
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8 queen puzzle unicolor variant
Since you can place 2•n-2 bishops on a n•n board, you can place maximally q = n - 1 queens on only the black squares of the board. (Drop the case n = 1.) (n = 5: 4 queens, so this is attainable.) Is ...
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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, $N$ $n$ ...
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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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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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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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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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Can I divide the candies among the kids so that everyone is happy?
I guess this is a dilemma every parent has to face at some point. And this time it was my turn. We were celebrating my daughter’s birthday and the time came to cut and share the cake. But, unlike the ...
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Partial knight's tour with crosslinks
We have many puzzles to find complete knight's tours – including on 4D boards, irregular boards and nonplanar boards – but few puzzles to find partial tours where only some cells are visited. I ...
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How many Full Kropki Sudoku solutions are there?
Kropki Sudoku is a variant where all consecutive adjacent numbers must be marked with a white dot between them, and all adjacent numbers with a 1:2 ratio must be marked with a black dot. (This is just ...
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Can my daughter’s candy preferences be modelled using numeric weights II?
My daughter wants to help. Recently she came to me and said:
"I am so sorry that you and your geeky friends have trouble modelling my candy preferences using numeric weights. So I have decided ...
user87015
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Are there other LEGO Duplo track layouts with two trains that trigger all the switches indefinitely?
My daughter has a LEGO Duplo railway set that she loves to play with. Here are some basic track elements in the set (I made the figures myself): the red element is a circular arc of 30°, the green ...
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