A Piece of the Pi: mathematics explained

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Repunits and prime numbers
A repunit (“repeated unit”) is a number that only contains the digit 1 in some number base.
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Richard Green
5
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
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
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
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
The comma sequence
The comma sequence (1 , 12 , 35 , 94 , 135 , 186 , 248 , …) is so called because the difference between successive terms is given by the digits on…
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Richard Green
5
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
Tredoku Patterns
Tredoku is a generalization of Sudoku in which each 3×3 box forms part of the surface of a 3-dimensional stack of cubes.
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Richard Green
5
The Rascal triangle
The Rascal triangle is a triangular array of numbers that is a variant of Pascal’s triangle.
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Richard Green
6
How to solve any maze using the digits of π
Is there a universal, deterministic sequence of actions that can solve any maze, assuming that the actions are applied blindly with no sensor feedback?
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Richard Green
10
Peaceable armies of queens
The peaceable queens problem is to determine the maximum number m such that one can place m queens of each colour on an n by n chessboard without any…
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Richard Green
9
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