Problem 1:

A bag contains beads of two colours: black and white. What is the smallest number of beads which must be drawn from the bag, without looking, so that among these beads, there are two of the same colour?

Problem 2:

One million pine trees grow in a forest. It is known that no pine tree has more than 600000 pine needles on it. Show that two pine trees in the forest must have the same number of pine needles.

Problem 3:

Given twelve integers, show that two of them can be chosen whose difference is divisible by 11.

More later. Kindly send your comments, answers, etc.

Nalin Pithwa