LongLiveYorke
Thursday, August 9th, 2007, 2:52 PM
QUOTE (coesillian @ Thursday, August 9th, 2007, 11:38 AM)

You are in a room where there are 100 coins on the ground, 10 of them are heads up and 90 of them are tails up. You need to divide the coins into two stacks that have the same number of coins heads up in each. You are blind and are unable to tells heads from tails by touch, what do you do?
I think this is the answer:
We have to take some amount of coins out of the group and flip them all. Though my motivation for this idea may seem arbitrary, you will see that it will work out:
So, let's say that out of our group of 100 coins, we choose x of them and form a group.
In the group we formed, let's imagine that we picked h heads (obviously h can not be more than 10 since there are only 10 heads from the initial group to choose).
So, in our new group, since we picked x coins and h of them are heads, we have:
Heads: h
Tails: x-h
Thus, in the remaining group (consisting of 100 - x coins) we have:
Heads: 10-h
Tails: (90-[x-h])
What we really want is a thing to do that does not depend on h, the amount of heads we choose in our pile. We want to determine a value of x coins to pick that doesn't depend on the number of h heads that will end up in our pile since we have no way of determining h.
We take our group of x coins that we picked out and flip them. Hence, we will have:
Heads: x-h
Tails: h
So, then number of heads in our new group is x-h. The number of heads in the remaining group (the 100-x coins that we didn't pick out of the initial group) is 10-h. Hence, we learn that we must select x=10 coins to pick out.
So, our solution is as follows: take our initial group of 100 coins, pick at random 10 of them, flip those 10 and the two groups should have the same amount of heads.
I think this is right...