Probl1

AlgKons

In this problem you have 12 spheres and a balance.

Part 1

It is given that one of the spheres is heavier than the others. What is the smallest number of weighings you need to guarantee to find the heavy sphere? What is your strategy?

Part 2

It is given that one of the spheres is heavier or lighter than the others. What is the smallest number of weighings you need to guarantee to find the sphere that differs in weight from the others? What is your strategy?

Part 2

It is given that one of the spheres possibly differs in weight from the others the others. What is the smallest number of weighings you need to guarantee to find the phere that differs from the others, if it exists, or to determine that all spheres have equal weight? What is your strategy?