Question 73
There is a number of toy kittens in a box. Each kitten has its head and tail painted with one of 2011 colors, not necessarily the same. One can take some kittens out of the box to form a collection. A collection is called "right", if it consists of exactly 2011 kittens so that their heads are painted with different colors, and their tails are also painted with different colors. We know that one can choose a "right" collection of kittens from the box in more than one way. Prove that some kittens (maybe none) can be removed from the box so that there are exactly two ways to choose a "right" collection of kittens from the remaining ones.