Chelsea Pensioners: the minimum who lost all four
Among a group of old soldiers, 70% have lost an eye, 75% an ear, 80% an arm, and 85% a leg. Lewis Carroll asks: no matter how these wounds happen to overlap among the men, what is the smallest percentage of the group that must have lost all four — an eye, an ear, an arm, and a leg?
Reveal the answer
At least 10%. Look at the complements instead: 30% still have both eyes, 25% both ears, 20% both arms, 15% both legs. Even if none of these groups overlapped at all, they'd only cover 30+25+20+15 = 90% of the men, so at least 10% can't belong to any of them — meaning they're missing none of an eye, ear, arm, or leg, i.e. they've lost all four. From Lewis Carroll's A Tangled Tale (1885), Knot X, "The Chelsea Pensioners."