February 2002, Stage 3&4

Problems

LOGO Challenge 9 - Overlapping Polygons

Stage: 2, 3 and 4 Challenge Level:

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

Have You Got It?

Stage: 3 Challenge Level:

Can you explain the strategy for winning this game with any target?

Getting an Angle

Stage: 3 Challenge Level:

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

Poly-puzzle

Stage: 3 Challenge Level:

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.

Concrete Calculation

Stage: 4 Challenge Level:

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. . . .

Lap Times

Stage: 4 Challenge Level:

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. . . .