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Use the fact that 4 and 7 have no common prime factors. If you run both timers at the same time, restarting each one whenever it rings, then sooner or later the seven-minute timer will go off two minutes after the four-minute timer did - and then you're in business.

In detail:

m0: start both timers

m4: timer 4 rings, restart it

m7: timer 7 rings, restart it

m8: timer 4 rings, restart it

m12: timer 4 rings, start cooking the egg

m14: timer 7 rings, restart it

m21: timer 7 rings, take out the egg.

The egg went in at minute 12 and came out at minute 21 - nine minutes of cooking.

This works because the 7-minute timer rang two minutes after the 4-minute timer did; the seven-minute timer times the last stretch. You can also make the 4-minute timer time the last stretch, and this is actually quicker (I just realized):

m0: start both timers

m4: timer 4 rings, restart it

m7: timer 7 rings, put in the egg

m8: timer 4 rings, restart it

m12: timer 4 rings, restart it

m16: timer 4 rings, take out the egg

The egg went in at minute 7 and came out at minute 16, which means it cooked for nine minutes.

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Q: With a seven minuet and a four minuet egg timer How do you boil an egg for nine minuets?
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