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And the way I ended up figuring this one when I read the solution was to take the 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 denomination is even. If you do that, it's easy because 4 times 5 is 20 and 4 singles will give you 24. Now you can do the other one because, okay, this is 9 and 21 and somewhere in there, you've got to come up with a difference. If you drop the number of 5 to 3 instead of 4 and add 6 singles, now you've got 21 dollars.