Explain why manhole covers are round. Why is this design better than, say, a square design.

Imagine you have eight balls, each of the same size.

One of the balls weights slightly more than the other seven.

Using a balance, find the heavier ball using only two weighings.

Imagine a bear walks the following paths:

1. South one mile
2. Left turn
3. East one mile
4. Left turn
5. North one mile

The bear arrives at where he started. What color is the bear? Why?

You are given a rectangular cake with a rectangular piece removed. The removed piece is of any size or orientation.

How would you cut the remainder of the cake into two equal halves with one straight cut of a knife?