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Anyways, 5 cents makes it easier to understand the pattern. Assuming the
same kind of pattern holds true for other integers, I hypothesize that
given denominations of a and b cents, where a and b are relatively prime,
the largest total you cannot make is ab-a-b. Obviously that's not divisible
by either a or b so you cannot make it. To complete the proof, I need to
show I can make all integers from ab-a-b+1 up to ab-a-b+min(a,b). I'll work
on it in my spare time, unless someone else first replies and gives me an
example to show my hypothesis is bunk and so I shouldn't bother.
ab-a-b. Obviously that's not divisible
by either a or b so you cannot make it.
Fabulous problem.
Never heard of it before. (How did you?)