perplexus.info :: Just Math : On the same floor

On the same floor (Posted on 2016-11-22)

How many solutions (m,n positive integers only) are there for
floor(m/6)=floor(n/13) ?

List them.

No Solution Yet Submitted by Ady TZIDON

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m, n < 50, corrected

| Comment 10 of 13 |

(In reply to m, n < 50 by Steve Herman)

For every n between 1 and 49, there are up to 6 m between 1 and 49 that satisfy the equation.

49 * 6 = 294

But this overcounts, because for n between 1 and 12, there are only 5 positive m that work (1,2,3,4,5).

Total solutions = 294 - 12 = 282, which has the advantage of agreeing with Ady's spoiler.

Posted by Steve Herman on 2016-11-23 08:29:06

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