February 2002, Stage 3&4

Problems

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GOT IT Now

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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LOGO Challenge 9 - Overlapping Polygons

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

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Getting an Angle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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Poly-puzzle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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Prime AP

Stage: 4 Challenge Level: Challenge Level:1

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference is divisible by 6. What if one of the terms is 3?

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Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .

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Lap Times

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .