Maths
posted by Mathsfreak .
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?

Are the runners arranged in any particular order? If not, then any two numbers might be next to each other. So only 1 runner can be used.
If we pick the lowestnumbered n runners, then since √1000 = 31.6, we need to make sure that all numbers are less than that. So, if there are only 31 runners, then no two numbers can multiply to be greater than 1000. 
I tried using circular permutations......but the answer didn't tally.Also..............31 is a wrong answer

well, there must be some other restriction on which numbers may be chosen, or how they may be arranged. I may have to get back to you on that.

In any order ,I guess, as it hasn't been particularly specified!The question is an exact copy from the springer book on 'Combinatorics'.

The question is an exact copy from the springer book on 'Combinatorics'.

Mind ur language,geezer.What on this earth is Brilliant anyways.Please check out 'The 1001 combinatorics problems' by 'Springer' problem #79 before blaming me..........:p
Respond to this Question
Similar Questions

5th grade math
A marathon race has 522 runners divided into 6 groups. What is a reasonable number of runners in each group? 
Maths
What is the sum of all integer values of n satisfying 1≤n≤100, such that n2−1 is a product of exactly two distinct prime numbers? 
Maths
What is the sum of all integer values of n satisfying 1≤n≤100, such that n2−1 is a product of exactly two distinct prime numbers? 
Maths
What is the sum of all integer values of n satisfying 1≤n≤100, such that n^2−1 is a product of exactly two distinct prime numbers? 
MATHS!!!Please HELP..:'(
What is the sum of all integer values of n satisfying 1≤n≤100, such that (n^2)−1 is a product of exactly two distinct prime numbers? 
math
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? 
Geometry
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
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
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
A total of 45 412 runners participated in the Vancouver Sun Run. Of these runners, 0.85% completed the run in under 40 min. How many runners completed in under 40 mins?