Newsletter #48 - Solution

Problem

What is the minimum number of pairwise comparisons needed to identify the heaviest and second heaviest of 128 objects?

Solution - by Anonymous

133 comparisons.

You need 127 comparisons to run a tournament of the 128 objects in a bracket. Then, the second-heaviest could only have been beaten by the heaviest, so you have 7 options. You can just weigh them pairwise, keeping the heavier one at each weighing, which takes 6 weighings.

Thank you!

Thanks to Peter (Toronto), Matt Lunix (Loveland, OH), and Ibrahim (California) for submitting solutions to this week's challenge problem.