OPM 2002

Consider five spheres with radius $10$ cm . Four of these spheres are arranged on a horizontal table so that its centers form a $20$ cm square and the fifth sphere is placed on them so that it touches the other four. What is the distance between center of this fifth sphere and the table?

The Blablabla set contains all the different seven-digit numbers that can be formed with the digits $2, 3, 4, 5, 6, 7$ and $8$ . Prove that there are not two Blablabla numbers such that one of them is divisible by the other.