[psyang]

Bring_Back_Shantz is the winner - congrats! For the bonus point, you should have mentioned that n (or x in your solution) needs to be even, otherwise it is impossible.

Spoiler!

So for the first question, divide the groups into 10 and 90, and flip the group of 10.
For n tails (where n is even), divide into n and 100-n and flip the n group.

Originally Posted by Bring_Back_Shantz

Spoiler!

You only need the same number of Tails (not heads & tails that is the important bit).

If the number of Tails in the original group is T then you put the coins into 2 groups.

Group 1:
# of coins: T
# of Tails (Call this TG1)= x
# of heads (Call this HG1) = T-x

Group 2:
# of coins: 100 (or whatever # of coins you started with) - T
# of Tails (call this TG2): T-x (this matters)
# of Heads: (100-T) - (T-x) = 100-2T+X - This doesn't really matter

Now flip all the coins in Group 1 the number of heads and tails swap values.
TG1 now equals T-x
HG1 now equals x

So now we have
TG1 = T-x = TG2