HKN : discover your destiny

Suppose you are seated in a dark room and on the table in front of you are placed ten coins – 3 heads up and 7 tails up.

The task @ hand is to separate these coins into two piles such that both piles have the same number of heads up coins.

Instructions : The room is dark. So obviously you cant see if a coin is heads up / tails up. Neither can you tell the difference by touching the coin. But to make your task a tad simpler – flipping the coins is always allowed.

That’s it. All set. Let’s flex that mind !

Solution:

Separate the coins into two piles of 3 and 7 each. We obviously don’t know of the number of heads / tails in each pile.

Take the smaller pile of 3 coins. Flip all the coins in this pile.

Now, both the piles will have the same number of heads.

How? It’s like this…

Let’s say the pile with 3 coins has ‘h’ heads. The total number of heads-up coins being three, the pile with 7 coins will have ‘3-h’ heads up. Hence, number of heads in the 3 coins pile is ‘h’ and number of coins in the 7 coins pile is ‘3-h’.

Now, take the smaller pile of 3 coins. Here, number of heads-up coins is ‘h’ and number of tails up coins is ‘3-h’ (because total number of coins in the pile is 3 and if ‘h’ of them are heads-up, only ‘3-h’ of them can be tails-up). When you flip all the coins here, all the coins which were previously heads become tails and vice versa. Hence, now the number of tails up coins here would be ‘h’. Therefore, number of heads up coins would be ‘3-h’.

Now, both piles have same number of heads up coins i.e. ‘3-h’.

Hence, problem solved !!