Although he is known primarily as a physicist, Albert Einstein did make at least one very important contribution to modern mathematics. In which field was this contribution?

On a plane, a map is drawn so that the border of any two intersecting areas is more than just one point. You wish to color the map so that two intersecting area have different colors. What is the minimal number of colors you will need to color any such map?

A “combination lock“ has three integers. Each integer is a member of this set: {0, 1, 2, 3, 4,}. How many such locks with different combinations can be made?