Visualising - March 2009, Stage 5

This month our problems require you to visualise. We use visualisation almost every time we engage in problem solving, for example to 'step into' a problem, to model a situation, to plan ahead, to support arguments and to communicate ideas.

Problems

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Snooker Frames

Stage: 5 Challenge Level: Challenge Level:1

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

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Polite Numbers

Stage: 5 Challenge Level: Challenge Level:1

A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?

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Five Circuits, Seven Spins

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

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In Between

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the solution to this algebraic inequality?

Elsewhere...