Problem solving and the pigeonhole principle
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Date
2007
Authors
Ching Ching, Wong
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Abstract
Over the years, problem solving has become one of the major concerns at all level of
school mathematics. In fact, in 2003, the Malaysian Ministry of Education suggested
that problem solving be the mai1;1 focus in the school mathematics and all mathematics
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teachers were_ advised to give specific consideration towards problem solving whilst
planning and teaching a particular subject topic.
In view of the importance of problem solvmg, this project aims to discuss some related
topics of problem solving such as the famous Polya's four-step problem solving
process, some strategies that may be useful to solve problems and finally, one of the
very important fundamental tactics of problem solving, i.e., the pigeonhole principle.
'If (n + 1) pigeons are put into n pigeonholes, then at least one of the holes has more
than one pigeon.' This is the simplest formulation of the pigeonhole principle. The basic
idea behind the pigeonhole principle may seem easy and common sense, but in the
hands of a capable mathematician it can be made to do uncommon things. In this
project, we not only look into the history and ideas of the pigeonhole principle, but we
also present several applications of the pigeonhole principle that will show us that the
principle is in fact a very powerful tool. Some activities related to the applications of
pigeonhole principle that can be carried out in the classroom are also suggested. In
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short, after reading this report, we hope that the readers will be fascinated by the
marvellous applications of the pigeonhole principle.