Weighing scales

Can you work out how many spheres will balance a single pyramid?

Age

14 to 16

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

Two pyramids and a sphere on one side of a pair of scales will just balance a cube on the other side.

A sphere and a cube together will just balance three pyramids.

How many spheres will just balance a single pyramid?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.