John Conway: 4 puzzles worth knowing

4 puzzles from John Conway, 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
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
An angel who can leap any distance, chased forever by a devil one square at a time
On an infinite chessboard, an 'Angel' of power k can fly up to k squares in any direction each turn, while a 'Devil' can block one square per turn, trying to eventually trap the An…
— John Conway (proofs by Bowditch, Máthé, Kloster), The Angel Problem

Five ideas worth knowing, every week