Puzzles
A sultan's 100 daughters, and only one chance to pick the best dowry
You'll meet 100 candidates one at a time, in random order, and see each one's value immediately. You must accept or reject on the spot, no going back. What strategy gives you the best odds of picking the single best candidate of all 100?
Reveal the answer
Reject the first 37 outright (about 1/e of the total), then accept the next candidate who beats everyone you've seen so far. This gives roughly a 37% chance of picking the very best, the highest odds any strategy can guarantee. Martin Gardner posed it as the 'Sultan's Dowry' in his February 1960 Scientific American column; mathematicians call it the secretary problem.
— Martin Gardner, Mathematical Games (Scientific American column) — Scientific American, February 1960