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July 21 Information
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).
| Mathematics desk | ||
|---|---|---|
| < July 20 | << Jun | July | Aug >> | July 22 > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
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| The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
July 21 Information
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).