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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Lap Times

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 track.

Doesn't Add Up

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

Two prompts :
  • Cut an 8 by 8 square into the four pieces and rearrange them as shown
  • What is the area of each piece ?