Posted by **Dan** on Sunday, June 23, 2013 at 11:23pm.

There are 100 runners, each given a distinct bib labeled 1 to 100. What is the most number of runners that we could arrange in a circle, such that the product of the numbers on the bibs of any 2 neighboring runners, is less than 1000?

- Math -
**MathMate**, Monday, June 24, 2013 at 6:43am
Since 31^2=961<1000, and 32^2=1024>1000 we can have a maximum of 31 pairs of numbers whose product would be less than 1000.

So the maximum number of runners would be 62.

- Math -
**Brilliant**, Wednesday, June 26, 2013 at 10:12am
Sorry man, can u reduce ur answer by 1. Because it is a circle, not a sequence.

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