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You are blindfolded and 10 coins are placed in front of you on the
table. You are allowed to touch the coins but can't tell which way up
they are by feel. You are told that there are 5 coins head up, and 5
coins tail up but not which ones are which.
How do you make two piles of
coins each with the same number of heads up? You can flip the coins
any number of times.
This is how it can be done!
What was the task?
Without thinking too much we need to make 2 piles of 5 coins each. Now there are 3 possibilities here depending on number of heads in either pile. One of the pile might have either 0 or 1 or 2 heads (other having 5 or 4 or 3 heads).
Case 1 :
P1 : T T T T T
P2 : H H H H H
Case 2 :
P1 : H T T T T
P2 : H H H H T
Case 3 :
P1 : H H T T T
P2 : H H H T T
Now just flipping all the coins from single pile will make number of heads (or say tails) in both piles equal. So we can flip coins of either P1 or P2. Let's flip all coins of P2.
Case 1 :
P1 : T T T T T Number of heads - 0
P2 : T T T T T Number of heads - 0
Case 2 :
P1 : H T T T T Number of heads - 1
P2 : T T T T H Number of heads - 1
Case 3 :
P1 : H H T T T Number of heads - 2
P2 : T T T H H Number of heads - 2
