A Piece of the Pi: mathematics explained

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Combinatorics 🧮

The Parks puzzle
The Parks puzzle is a Sudoku-like game that is played on a square grid containing different coloured regions known as parks. The objective is to place…
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Richard Green
Hexagonal knot mosaics
A hexagonal knot mosaic is a way to draw a knot on a hexagonal board.
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Richard Green
7
Penny graphs
A penny graph can be created from a non-overlapping arrangement of unit circles on a flat surface.
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Richard Green
2
Misère Connect Four
It is well known that it is impossible to win at noughts and crosses (tic-tac-toe) unless your opponent makes a mistake, because if both players play…
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Richard Green
3
Ulam words and the Ulam sequence
The Ulam sequence is a sequence of positive integers xn, where x1=1, x2=2, and where each xn for n > 2 is defined to be the smallest integer that can be…
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Richard Green
5
How many triangles are there?
A well-known type of brain teaser invites the reader to count the number of triangles formed by dividing up a larger triangle using straight lines.
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Richard Green
3
Facially complete graphs
The Four Colour Theorem proves that no more than four colours are required to colour the regions of any map in such a way that no two adjacent regions…
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Richard Green
8
Wherever you go, I win!
In theory, the objective of chess is to capture the king, but in practice, the game ends two moves earlier in the position of checkmate. We can imagine…
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Richard Green
2
Tilings and metallic means
Two of the most famous two-dimensional models of quasicrystals are the Penrose rhomb tiling and the Ammann–Beenker tiling. Each of these types of tiling…
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Richard Green
2
Permutation Wordle
In the well-known game Wordle, a player has six attempts to guess a five-letter English word.
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Richard Green
3
Solving a maze with two exits
Given a maze based on a square grid with an entrance at A and two exits at B and C, is there a navigational strategy that guarantees a 50% probability…
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Richard Green
Maximally even musical scales
Given a musical scale, is there any way to measure the extent to which the notes are evenly spaced?
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Richard Green
4
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