One poisoned bottle hides among a thousand. You have ten tasters and a poison that acts within the hour. Brute force means a thousand sips. Information theory does it in a single round, by turning each person into a bit. Number every bottle from 0 to 999 in binary. A thousand labels fit inside ten binary digits, because 2^10 = 1024. Assign each taster to one bit position, from bit 0 up to bit 9. The rule is purely mechanical: - Taster i sips from every bottle whose binary label carries a 1 in position i - Each person ends up drinking a cocktail drawn from hundreds of bottles at once - Wait for the poison to act, then read off who falls ill Take bottle 742. In binary that is 1011100110. Tasters 1, 2, 5, 6, 7 and 9 all sip from it, so if 742 is the guilty one, exactly those six collapse and the remaining four stay standing. The pattern of sick and healthy tasters is a ten-bit word. A collapsed taster marks a 1, a survivor marks a 0. Line them from bit 9 down to bit 0 and you have re...