A drawer of loose socks and gloves: how many must you grab blind for a matching pair?
A dark drawer holds 10 pairs of brown socks and 10 pairs of black socks, all unpaired and mixed loose. A second drawer holds the same split of brown and black gloves — except gloves also come left- and right-handed. Reaching in blind, what's the fewest socks you must pull out to guarantee a matching pair? And the fewest gloves, to guarantee a matching pair you can actually wear?
Reveal the answer
Just 3 socks: with only two colours, a third sock must repeat one of the first two. Gloves need 21: with colour and hand together making four categories, you could unluckily draw 20 all-left-hand gloves (10 brown, 10 black) before a 21st forces a wearable match. Yakov Perelman set this out as an everyday case of the pigeonhole principle in his puzzle collection Figures for Fun.
— Yakov Perelman, Mathematics Can Be Fun (Figures for Fun) — Part One, Puzzle 27