Solving Together - Combining Lengths

Age 11 to 14

In this puzzle, work together to explore the lengths you can make using three rods.
Watch the video for an introduction, or scroll down to explore.



Alternatively, here are some instructions.

Take it in turns to choose three rods, and see which lengths you can make with them.
Can you find a set of three rods that you can use to make any length from 1 to 10?





It's possible to find a set of rods that measures even more than ten different lengths.
Can you find a set of three rods that you can use to make any length from 1 to 11? Or 1 to 12?
What's the furthest that you can go?


How many different lengths could you make if you only had two rods?
How many different lengths do you think you could make using four rods?


Note for parents: You may find it useful to watch our Guidance for Parents video for advice on how to get the most out of the Solving Together resources.

Combining Lengths explores the mathematical areas of combinatorics and ternary arithmetic. It builds important problem solving skills, such as working systematically.