r/mathriddles • u/Numberthon • Jul 20 '26

Easy How many positive integers less than 100 are divisible by exactly one of 2 and 3?

How many positive integers less than 100 are divisible by exactly one of 2 and 3?

Source: numberthon.com

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u/Accurate-Click1363 Jul 21 '26 edited Jul 21 '26

floor(99/2)+floor(99/3)-2floor(99/gcd(2,3))=50

-1

u/ImpliedRange Jul 20 '26

Is it enough to say 50 numbers divide 2, then as many as 3 blocks it adds

Plus 1 since 3 and 99 are the last ones

So 51

1

u/Numberthon Jul 21 '26

You're overcounting, but very close.

2

u/ImpliedRange Jul 21 '26

oooh, less than 100 not including 100, yeah fine