Simple question?

[Amid Cent]

I was trying to figure out how many possible results can be achieved by playing 2 10-person SNG's at the same time.

Intuitively, the answer should be: 10 finishes in the first tournament times 10 in the second. Then divide by 2, since order does not matter. That gives you 100/2 = 50.

However, the correct answer is actually 55. You can get this by sort of "freezing" the first finish, and counting each finish in the second. You then get 10 + 9 + 8 + ... + 1 = 55.

Is my logic in the first paragraph way off? Or did I just assume incorrectly?

Thanks.

[elitegimp]

your logic is fine, you just have 10 times that you finish in the same position (10-10, 9-9, ..., 1-1) that you only counted 5 times by dividing everything by 2.

(edit: so the logic would be 10 places to finish in tourney 1 * 9 _diff_ places in tourney 2 /2 = 45 + 10 finish in same spot = 55)