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And for the way I ended up figuring this one when I wrote a solution was to fix a even number. And realize that the simplest thing would be since the answer is even. The most likely thing is that the number of bills in each nomination is even. If you do that it's easy because four times five is twenty and four singles will give you twenty-four. Now you can do the other one because okay this is nine and twenty-one and somewhere in there you've got to come up with a difference. If you drop the number of five to three instead of four and add six singles now you've got twenty-one dollars.