Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# The Great Weights Puzzle

## You may also like

### Instant Insanity

### Magic Caterpillars

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 14 to 16

Challenge Level

This problem follows on from 9 Weights

You have twelve weights, one of which is heavier or lighter than the rest, but you don't know which one is heavier or lighter, and a balance. Using just 3 weighings on the balance, can you find a way to identify which weight is the odd one out, and whether it is heavier or lighter?

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.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.