This problem is closely related to the Frobenius coin problem: http://en.wikipedia.org/wiki/Coin_problem http://en.wikipedia.org/wiki/Coin_problem It's an inte

This problem is closely related to the Frobenius coin problem: http://en.wikipedia.org/wiki/Coin_problem http://en.wikipedia.org/wiki/Coin_problem It's an interesting problem. My gut reaction was to solve X1 + X2 + (...) + X6 = 200; X1, ..., X6 < 0, which would be C(205, 200), but that ignores the denominations of each coin, so it doesn't really generate what you want.