O princípio da casa de pombos e a contagem dupla

Abstract

In combinatorics, there are two types of problems: the existence and the count. Is it quite fascinating and at the same time challenging, because even the teachers more agile overlap in certain problems. With that, in some cases we use a bit of intuition and logic to solve different problems, and then enters the pigeonhole principle and the Double Count. These two are extremely useful topical both in problem solving, as in the demonstration of certain theorems, are in number theory or even in geometry. The pigeonhole principle is based on the fact that if we have n objects to be distributed in k drawers, where n is greater than k, then at least one of the drawers will house at least two objects. This obvious fact, that any child understand, should not be underestimated, since, as we shall see in chapter one, he has a great power to solve problems of existence. The Double Count is based on a count of two distinct ways in a particular situation and that result in the same outcome. Thus, the two concepts presented become quite obvious, but essentially useful in understanding mathematical logic.