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Myr's "Math Problem of the Week":
You are shipwrecked and captured by cannibals. Two hourglasses are given to you. One measures exactly four minutes, the other exactly seven minutes. The chief of the cannibals says you must tell when exactly nine minutes have passed. If you can do this, you may go free. If you can't -- you're dinner. The chief yells, "Start now!"
What do you do?
Flip both hourglasses over. When the four-minute timer runs out, flip it back over. Four minutes have passed. When the seven-minute timer runs out flip it over. Seven minutes have passed. There is now one minute left on the four-minute hourglass. When it runs out eight minutes have passed and there is one minute of sand in the bottom of the seven-minute hourglass. Flip the seven-minute hourglass over and when that one minute of sand runs out, you have timed nine minutes exactly.
You are shipwrecked and captured by cannibals. Two hourglasses are given to you. One measures exactly four minutes, the other exactly seven minutes. The chief of the cannibals says you must tell when exactly nine minutes have passed. If you can do this, you may go free. If you can't -- you're dinner. The chief yells, "Start now!"
What do you do?
Flip both hourglasses over. When the four-minute timer runs out, flip it back over. Four minutes have passed. When the seven-minute timer runs out flip it over. Seven minutes have passed. There is now one minute left on the four-minute hourglass. When it runs out eight minutes have passed and there is one minute of sand in the bottom of the seven-minute hourglass. Flip the seven-minute hourglass over and when that one minute of sand runs out, you have timed nine minutes exactly.
