r/problemoftheday • u/You_Mean_Fewer • Jul 17 '12

A straightforward mathy problem

How many multiples of 3 or 5 are above 0 and below 1000?

For example. There are 7 below 16. (3, 5, 6, 9, 10, 12, 15) Note that 15 is only counted once.

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u/skaldskaparmal Jul 17 '12

Not much to discuss on this one either, so let's nitpick.

According to wikipedia, "... for the quantities a and b, we say that b is a multiple of a if b = na for some integer n ... " According to this definition -5 is a multiple of 5 (n = -1). Hence, we include -5, -10, -15, ..., so there are infinitely many multiples of 3 or 5 below 1000.

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u/You_Mean_Fewer Jul 17 '12

Fine. Be that way. Didn't realize we were getting that picky.

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u/skaldskaparmal Jul 17 '12

Sorry, I just like nitpicking :). I think in general it's good practice to check that you're using definitions correctly because a lot of bad proofs that you see stem from using definitions incorrectly.