Princípios de contagem e aplicação do princípio aditivo: o problema de contagem dos quadrados em uma quadrícula e o código qq

Abstract

The present dissertation intends at first to approach the elementary Principles of combinatorics, giving a focus on problem solving without the direct use of ready-made formulas, and in some cases constructing them in order to show that problem solving involving combinatorial requires more of a good idea than of the knowledge of certain standard procedures of resolution. The other point to be highlighted in this work was motivated by a problem seen in a contest of the Federal Institute of Ceará that asked to determine the number of distinct squares, sides not necessarily parallel to the Cartesian axes, whose vertices belong to the set {(a, b); a and b integers, 1≤a≤7; 1≤b≤7}, a problem of counting using the Addition Principle, which will be initiated in this work very simply by points in a line and the count of segments, going through the problem just like the one in the contest but with a grid 10 X 10 until its version in three dimensions with the counting of cubes inserted in it and with the conjecture for n-dimensional spaces. Additionally, an application for this square counting problem is presented in a transformation of these into a read-through type code called by the author of Code QQ (Square squares).