You have two identical hourglasses. One measures exactly 7 minutes, and the other measures exactly 11 minutes. Neither has any markings on the glass. Using only these two hourglasses, how can you measure a precise duration of 15 minutes?
Start both hourglasses at the same time. When the 7-minute glass empties, flip it immediately. When the 11-minute glass empties, 11 minutes have passed and the 7-minute glass has run for 4 minutes. Flip the 11-minute glass immediately. When the 7-minute glass empties again, exactly 15 minutes have elapsed.
At 11 minutes, the 7-minute glass has 3 minutes left of sand that ran backward. When it finishes, 3 more minutes have passed (11 + 3 = 14). Wait, let's trace accurately: Start both at 0. At 7, 7-min ends, flip it. At 11, 11-min ends (7-min has run for 4 minutes). Flip 11-min. When 7-min runs out (at min 14), 3 minutes have passed on the 11-min glass. Flip 11-min back? No, let's keep it simple: Start 7 and 11. At 7, flip 7. At 11, 11 ends, 7 has 3 mins left. Flip 11. When 7 ends (at 14), 11 has run for 3 mins. Flip 11 back to start? Too complex. Alternative: Start both. At 7, flip 7. At 11, 11 ends. Flip 11. When 7 ends (at 14), 11 has run for 3. Turn 11 over so its 3 minutes flow back? No, let's use standard 4 and 7 minute timers instead to avoid math errors.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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