[Bring_Back_Shantz]

Originally Posted by 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.

I assume you mean "T" in my solution.
As in the starting number of tails in the total group.
But that's not correct, it can definitely be odd.
Look at the extreme example where n = 1 (1 starting tail)

Group 1 will be 1 coin.
Group 2 will be 99 coins.

There are 2 possibilities
1:
Group 1 = 1 tail
Group 2 = 99 heads

Flip over the coin in group 1
Group 1 = 1 head = 0 tails
Group 2 = 99 heads = 0 tails

2:
Group 1 = 1 Head
Group 2 = 1 tail, 98 heads

Flip over the coin in group 1
Group 1 - 1 tail
Group 2 = 1 tail, 98 heads

Works just fine for an odd number.