Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Euler's Officers

## You may also like

### Doodles

Or search by topic

Age 14 to 16

Challenge Level

How many different solutions can you find to this problem?

Arrange 25 officers, each having one of five different ranks $a$, $b$, $c$, $d$ and $e$, and belonging to one of five different regiments $p$, $q$, $r$, $s$ and $t$, in a square formation 5 by 5, so that each row and each file contains just one officer of each rank and just one from each regiment.

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?