Wikipedia:Reference desk/Archives/Mathematics/2011 July 21

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July 21

Number theory

I saw a problem that goes like this: John tries to arrange some marbles in a rectangle. He finds that he needs two more to put them in a rectangle with 8 columns and three more to put them in a rectangle with 9. Exactly how many marbles does he have, given that he has between 100 and 200? In both arrangements, the last column has 6 marbles, which means I'm looking for a number in decimal which ends in 6 in both bases 8 and 9. I figure I could solve it using bases, but I haven't been able to figure out how. Can someone help? (How I really solved it: anything divisible by both 8 and 9 is also divisible by lcm(8,9), 72 since 8 and 9 are coprime, which implies that anything that has the same remainder when divided by 8 and 9 has that remainder when divided by 72. The only number like that between 100 and 200 is 150=72*2+6) — Preceding unsigned comment added by 24.92.88.206 (talk) 23:21, 21 July 2011 (UTC)

No, using bases only increases the confusion. You solved the problem yourself. Bo Jacoby (talk) 11:39, 22 July 2011 (UTC).