RobinZ comments on Open Thread: March 2010, part 2 - Less Wrong
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I tested myself with MATLAB (which makes it quite easy) out of some unnecessary curiosity - it took me about seven minutes, a fair part of which was debugging.
I feel rather ashamed of that, actually.
As everyone else seems to be posting their code:
A better program (by which I mean "faster", not "clearer" or "easier to modify" or "easier to maintain") would replace the tests with something less intensive - for example, incrementing two counters (one for 3 and one for 5) and zeroing them when they hit their respective desired factors.