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Problem of the Week 1167

Unlock the Safe

A certain lock has three wheels, A, B, C, each of which can be set to 8 positions. But the lock will open when any two of the wheels point at the correct number. So it is easy to open the lock in 64 tries by just trying all the possibilities for the A and B wheels.

Show how it can be done in a much smaller number of tries.

Source: East German Olympiad problem, Crux Math. 1988. Also in Ross Honsberger's book, From Erdos to Kiev, MAA.

© Copyright 2013 Stan Wagon. Reproduced with permission.

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9 October 2013