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A Hundred Lockers

Posted by ubpdqn on April 3, 2011

Willy Wonka visits a school. There are a bank of 100 lockers and Willy has hidden prizes in certain lockers.  He invites the children to work out where he has hidden the  prizes.

At the start all the lockers are opened. Then for every multiple of 2, 3, … ,100 Willy’s assistant will close the locker if it is open or open it if it is closed.  So, after opening all the lockers, for multiples of  locker 2,4,6,…,100 will be closed. The multiples of 3 are done next and so on.

Willy has hidden the prizes in the lockers that are open at the end of this process.

He asks if you can  tell me which lockers will be open at the end then you will get the prize.

One child promptly exclaims there are 10 lockers open and they are…

What did the child answer?

Open lockers has the answer.

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