# Questions tagged [combinatorics]

A puzzle based on combinatorics, which is the study of counting discrete structures. Use with [mathematics]

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### Running Out of Digits, Level 3

The challenge idea is credited to HelloWorld1337. You initially have x of each digit from 0 to 9. This means you have x * 10 digits in total. This count for each digit is shown in the table below. ...
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### Covering a 15x15 grid with rectangles

You are given a 15x15 grid and asked to cover it with rectangles whose dimensions are a power of 2. For example you can use rectangles 8x1 and 4x4, but not 2x3. The rectangles must cover every cell of ...
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### Grid infection with diagonal adjacencies

A community consists of 81 houses laid out in a 9 x 9 square grid. Every household is friends with their eight orthogonal and diagonal neighbors (except for the houses on the perimeter which have only ...
665 views

### Domino tiling on 8x8 checkerboard with four squares removed

I once posted this problem on the (now deleted) Area 51 Math Puzzles proposal. It was well-received there, but obviously I didn't get an answer. I still don't know the answer, and I'm not even sure if ...
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### The Greenhouse Problem version 2

This is an extension of Nilster's great puzzle: The Greenhouse Problem The task is the same, but this time sprinklers cover only a 3x3 square around them. For completeness, here is the full set of ...
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### How long will it take to hand out the shuffled papers?

A teacher has $n$ students sit in a circle in her classroom. She holds in her hands a perfectly shuffled stack of the students' graded homework, with Juan's on top. She is currently standing in front ...
289 views

### Mathematics for the English major

An entry in Fortnightly Topic Challenge #48: Unusual tag mix I was looking at the unusual tag mixes post, and one of the ones listed is combinatorics and english. I thought "who's going to be ...
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### How many triangles can you obtain using the 6 vertices and center of a regular hexagon?

Let's say there is a regular hexagon with center at point O. Question 1. How many triangles can you obtain using the 6 vertices and its center? Question 2. What is the largest number of different ...
186 views

### Variation of 100 Prisoners' names in boxes

100 Prisoners' Names in Boxes The following puzzle is a variation of the above puzzle. Names in Boxes The names of 4 prisoners are placed in 4 wooden boxes , one name to a box, and the boxes are ...
372 views

### Maximize my flags

You are given the next list of 48 flags. For each pair of flags that are side by side, you score 1 point per color they share as a frontier. For instance France and Finland score 1 point thanks to ...
138 views

### Presidential Election

This puzzle was inspired by the current 2020 US presidential election. You are running for president in a country with 10 states. To win a state you must conduct more rallies than your opponent. ...