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Três problemas sobre partições na Olimpíada Internacional de Matemática

2020; Lázaro, C. and Rodrigues, T.; Volume: 19; Linguagem: Inglês

10.21167/cqdvol19202023169664jll118127

2316-9664

Juan López Linares,

Mathematics Education and Teaching Techniques

Combinatorial problems, in general, and partitions in particular, are rarely discussed with elementary and high school students.However, this knowledge is important for success in competitions.In this article we discuss in detail three problems proposed for the International Mathematical Olympiad (IMO).In the first problem the greatest number of different rectangles, with an equal number of white and black squares, in which a chess board can be partitioned is sought.In the second problem one seeks to divide a square into other smaller squares and asks from which natural number this is always possible.In the third problem we discover how and when it is possible to divide a list of consecutive naturals into two of equal sum.To solve them one must use a mixture of several contents: arithmetic progression, formulate and solve inequalities, factoring, representation of integers in the division by two and four and logic.