Thursday, October 14, 2010

Interview Puzzle - Equal heads

Puzzle:

There are 50 coins on the table out of which 43 are tail-face up and 7 are head face up. You are blind folded and there is no way to determine which side is up by rubbing, etc. You have to divide the 50 coins in two sets (not necessarily equal) such that both have equal number of coins with heads face up.

Solution:

Divide the 50 coins into two sets - once set with 43 coins and the other set with 7 coins. Thus, the first set will contain 'x' heads and '43-x' tails and the second set will contain '7-x' heads and 'x' tails. The possibilities can be tabulated as shown in the left table.

Now, flip the coins in the second set, so that both will contain 'x' heads. The result after flipping can be seen on the right table. You can see that both sets have equal number of heads whatever be the distribution.


Cheers!!
Jack

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