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# Weighty Problem

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30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. That way the cabinet can be moved in a series of turns about one corner at a time.

Presently it is placed (on the X) facing in the direction of the arrows.

The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round (and still placed with its edge on the X). The corners of the cabinet do not always have to stand on the corners of the square tiles on the floor.

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.