Questions tagged [combinatorics]
A puzzle based on combinatorics, which is the study of counting discrete structures. Use with [mathematics]
898 questions
2 votes
0 answers
213 views
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 ...
- 21
7 votes
4 answers
604 views
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 ...
- 4,590
18 votes
3 answers
2k views
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 ...
- 5,195
4 votes
3 answers
728 views
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 ...
- 1,181
16 votes
3 answers
1k views
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 ...
- 20.3k
10 votes
1 answer
852 views
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 ...
- 427
7 votes
1 answer
253 views
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 ...
- 20.3k
5 votes
2 answers
363 views
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 ...
- 20.3k
3 votes
1 answer
279 views
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 ...
- 10.5k
10 votes
1 answer
701 views
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 ...
- 12.4k
8 votes
1 answer
780 views
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 ...
- 2,541
16 votes
3 answers
3k views
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 ...
- 20.3k
31 votes
6 answers
2k views
Lock company wants to prevent unauthorized key duplicates
A lock company produces a special pin tumbler lock which is marketed towards the prevention of unauthorized key duplicates. Each lock contains a unique combination of 5 key pins chosen from 10 ...
- 431
14 votes
8 answers
2k views
Snow White and the Seven Rooks on Dark Squares
With the white queen on a light-coloured square of your choosing, can you place 7 rooks on the dark squares of the chessboard so that no piece attacks another? In the above Lichess illustration (with ...
- 85.4k
26 votes
4 answers
2k views
Can I succeed in appraising the candies according to my daughter’s preferences?
My daughter has always been very picky when it came to food. Initially, I thought she made random choices, but after observing this for a while, I found a pattern in her preferences. Let me explain. ...
- 20.3k