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.

## Answer This Question

## Related Questions

- Math - There are 100 runners, each given a distinct bib labeled 1 to 100. What ...
- math - There are 100 runners, each given a distinct bib labeled 1 to 100. What ...
- Geometry - There are 100 runners, each given a distinct bib labeled 1 to 100. ...
- Maths - There are 100 runners, each given a distinct bib labeled 1 to 100. What ...
- MATHS!!!Please HELP..:'( - What is the sum of all integer values of n satisfying...
- 5th grade math - A marathon race has 522 runners divided into 6 groups. What is ...
- Physics - Distance runners often run around an approximately circular trajectory...
- math - Weekly mileage totals 24 runners 10 15 20 25 30 35 40 45 50 55 60 Max- 55...
- math - A runners time in the 100-dash is 32 seconds when rounded to the nearest ...
- math - If 453 runners out of 620 completed a marathon, what percent of the ...

More Related Questions