Richard Guy: 4 puzzles worth knowing

4 puzzles from Richard Guy, each explained in a minute and credited to the original work. Free on Savvy.

Checkers jump toward a target row. Can they ever reach the fifth row up?
Pegs sit on every square of an infinite checkerboard below a horizontal line. Each move takes one peg and jumps it over an adjacent peg in a straight line, removing the peg that wa…
— John Conway, Elwyn Berlekamp, Richard Guy, Winning Ways for Your Mathematical Plays
Work out the day of the week for any date in history, in your head, in seconds
What day of the week was 4 July 1776? Mathematician John Conway devised a mental algorithm, the Doomsday rule, that lets a practiced person answer questions like this for any date …
— John Conway & Richard Guy, The Book of Numbers
In a two-rule grid game, find a pattern that walks across the board forever
Conway's Game of Life runs on just two rules about which cells live or die based on their neighbours, applied to a grid, generation after generation. Most starting patterns fizzle …
— John Horton Conway (rules); Richard K. Guy (glider), Conway's Game of Life
Name a number no one's named before — but never be the one who says 1
Two players alternately call out a positive whole number that cannot be written as a sum of numbers already named (a number may be reused any number of times in that sum). For exam…
— Elwyn Berlekamp, John Conway, Richard Guy, Winning Ways for Your Mathematical Plays

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