# Questions tagged [combinatorics]

A puzzle based on combinatorial mathematics, which is the study of finite or countable discrete structures.

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### The most probable key

You broke into John Doe's house and found the safe. It has a combination lock with 4 dials ranging from 0 to 9 each. ...
1k views

### Possible pawn combinations

This may seem simple, but I have a problem calculating it. It may be because it's Monday morning. How may possible valid combinations of one color pawn (white or black, your choice) positions are ...
451 views

### Cover all squares in a square grid by moving to adjacent squares

Admittedly this is a problem I encountered from school but I cannot think of a proper proof solution. I thought about the logic that in order to cover all squares, there must be closed loops of ...
230 views

### Interesting card combinations [closed]

In a normal pack of playing cards (without jokers), the probabilities of the following events are the same: (1) Drawing a set of 4 different cards (irrespective of its color and suit) - let us call ...
372 views

### Jigsaw Logic: ?s galore

I am working on a 256 piece jigsaw puzzle, but I am having a lot of trouble. Instead of the picture being a landscape or painting, the final image is just a sixteen by sixteen grid of identical ...
172 views

### Arrange six cigarettes in such a way that each cigarette touches every other cigarette [duplicate]

What are some ways to arrange six cigarettes in such a way that each cigarette touches every other cigarette?
194 views

### 15 pawns on a chessboard

15 pawns are placed on the centers of distinct squares of a chessboard. Prove that there are three pawns which form a right triangle. In the example board below, a couple of right triangles are ...
4k views

### bored of eating soup

A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating. When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
259 views

### 222 Black and 333 white balls [duplicate]

You have a bag with 222 black balls and 333 white balls in it. You also have an almost infinite supply of black and white balls that are not in the bag. You do the following over and over again: ...
307 views

### Simple solution for a scheduling puzzle

An amateur football coach wants to train the players by dividing them into two team and having the teams play each other. However, because of time constraints, each player comes and leaves at a ...
530 views

### Find the smallest positive integer that cannot be made from four 8s, or show it doesn't exist

This puzzle was inspired by one recently posted by @Max. What is the smallest positive integer that cannot be made from four 8s, where bracketing is allowed and the only permitted operations are ...
681 views

### Crystal Maze totem pole puzzle

The UK game show "The Crystal Maze" features a puzzle based around a totem pole. The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be ...
200 views

### Which string can't be accessed? [closed]

We start from the string $ABCDEF$ and we can edit it with the following rules: 1.$ABCDEF \Rightarrow ADBECF$ 2.$ABCDEF \Rightarrow DAEBFC$ Which string can't be accessed? DBAFEC ...
139 views

### Rotating teams without repeating [closed]

I have 24 teams that will rotate to 12 stations (2 teams per station) Teams will not compete against another team more than once.
### Divide $n$-gon into triangles
Find all positive integer $n \geq3$ such that the convex $n$-gon can be divided by its $n-3$ diagonals into $n-2$ triangles so that no two of these diagonals intersect inside the $n$-gon and all the ...