Solving Problems - The Problem Solving Cycle

The Problem Solving Cycle

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Question:

The authorities of a team sport are planning to hold a World Cup competition. They need to decide how many teams will come to the host country to compete in the 'World Cup finals'.

The World Cup finals will start with a number of groups. In a group, each team plays every other team once. One or more from each group will qualify for the next stage.

The next stage is a knock-out competition from which one team will emerge as the world champions.

Every team must be guaranteed at least three matches to make it financially viable for them to take part.

To ensure a suitable length of competition, the winners must play exactly seven matchs.

How many teams can take part in the World Cup finals?

What general rules apply to the number of teams in a competition like this, involving groups and then a knock-out stage?

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1. Problem specification & analysis

• First, formulate the problem in a way which allows mathematical methods to be used.
• Then, analyse the problem and decide how to go about answering it.

Specification e.g.

The question specifies that every team must play at least three matches.

The question specifies that the winners must play exactly seven matches.

Analysis e.g.

DECIDE THE IMPORTANT VARIABLES.

• The number…