Question:
There is a large* pile of coins in a room. Almost all of them are turned heads up,
except just 20 which are turned tails up. You know this, but are wearing a blindfold
and gloves (which cannot be removed) so you have no way of telling which are heads
and which are tails.
The challenge: split the coins into two groups, such that both groups have the same number
of coins which are tails up. How would you achieve this?
*it can be assumed that there are infinitely many coins.
Hint: the piles do not have to be the same size, which makes sense as the original pile is endless!
Answer: (click to show)
Take any 20 coins from the pile and turn them all over to the opposite face. Now you have
completed the challenge!
This works because:
Of the 20 coins you chose, x are tails, where x is between 0 and 20. In the large
pile there were originally 20 tails, but now there are 20-x tails. You've taken 20-x
heads from the large pile, and turned them over to be tails.
So now there are 20-x tails up coins in each pile!
