He can't have any twenties, since you can't make $5 with 9 bills.
He can't have 2 tens, since you can't make $5 with 8 bills.
So he either has 1 ten or no tens.
I. He has 1 ten.
He has to make $15 with 9 bills.
He can't have 2 fives, because you can't make $5 with 7 bills,
A. He has 1 five.
He has to make $10 with 8 bills.
That's impossible to do with $1 bills, so he has to use $2 bills.
He can only do that with 6 ones and 2 twos.
So there is one solution:
1. 1 ten, 1 five, 2 twos, and 6 ones.
B. He has 0 fives.
He has to make $15 with 9 bills.
He can't do that with ones only, so he has to use twos.
The only way is 6 twos and 3 ones.
So there is another solution:
2. 1 ten, 6 twos, 3 ones.
II. He has 0 tens.
He can't just have 1 five, because he'd have to make #20 with 9 bills.
And even if he used all twos that would only be $18.
A. He has 2 fives.
He has to make $15 with 8 bills.
That's easy. 7 twos and 1 one. So that's a third solution.
3. 2 fives, 7 twos, and 1 one.
B. He has 3 fives.
He has to make $10 with 7 bills.
He can only do that with 3 twos and 4 ones. That's the last way:
4. 3 fives, 3 twos, and 4 ones.
There are four solutions. All four require two dollar bills.
Edwin
