HOW TO BREAK IN SMALL PIECES AN INTERNATIONAL MATHEMATICAL OLYMPIAD PROBLEM?

Universidad Autonoma del Estado de Morelos (MEXICO)

Appears in: EDULEARN14 Proceedings

Publication year: 2014

Pages: 6342-6346

ISBN: 978-84-617-0557-3

ISSN: 2340-1117

Publication year: 2014

Pages: 6342-6346

ISBN: 978-84-617-0557-3

ISSN: 2340-1117

Conference name: 6th International Conference on Education and New Learning Technologies

Dates: 7-9 July, 2014

Location: Barcelona, Spain

Dates: 7-9 July, 2014

Location: Barcelona, Spain

decompose a problem into several much easier questions, that together solve the original problem. This decomposition implies to make a list of simple

and natural questions for the student, and once he answers them, he reaches a complete solution of the original problem. All the answers help him

to solve the original problem. The correct solution has to be reach by the students with the help of the discussion between them, the professor only stands

as a guide, but he is not allow to give the answer. It is a very detailed process that allows us to see all the characteristics of the problem and to analyze how the

hypothesis can be used in a correct and efficient way to get to the final solution. In this paper, we explained this process and we apply it to solve a problem

that appeared in the Short list of proposed problems for the IMO (International Mathematical Olympiad) in 2009. The problem is the following:

"Five identical empty buckets of 2-liter capacity stand at the vertices of a regular pentagon. Cinderella and her wicked Stepmother go through a sequence

of rounds: At the beginning of every round, the Stepmother takes one liter of water from the nearby river and distributes it

arbitrarily over the five buckets. Then Cinderella chooses a pair of neighboring buckets, empties them into the river, and puts them back.

Then the next round begins. The Stepmother’s goal is to make one of these buckets overflow. Cinderella’s goal is to prevent this. Can the wicked

Stepmother enforce a bucket overflow?"

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