Sorry for the long wait, I'm back with more problems !
Last time, I saw the following problem which is briefly explained, but not that easy to answer :
So if your answer is K, you need to :
Last time, I saw the following problem which is briefly explained, but not that easy to answer :
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?*
For instance, I can always arrange 10 people numbered 1 to 10 in a circle without no worries, because the maximum product of 2 neighboring runners is then 9*10 = 90 < 1000. One can always guess the answer, but the complete solution to this problem is a beauty (at least that's what I found myself).
So if your answer is K, you need to :
a) Give a possible configuration of K people fulfilling the above's criteria
b) Prove that if you take more than K people, you can't arrange them in such circle
Hurry, the runners are waiting !
*Retrieved from https://brilliant.org/assessment/new_solvable_pos/geometry-and-combinatorics/6/#_=_
