Mathematical Investigation

Number Stairs

Look at the shape that looks like stairs on the big 10x10 grid. It has 3 steps. If you add up all the numbers inside it, you get 194.

A 3-step stair hanging from 45 has a stair total of 194.

Try this with other 3-step stairs by clicking numbers on the grid. Can you see a pattern between the total number and where the stairs are hanging?

Now, try looking at stairs with different numbers of steps on different grids. Can you find a pattern with those totals?

rows and columns

2-step 3-step 4-step 5-step

Adapted from a resource created by D.Keith at and shared with a creative commons licence.


Teachers' notes for this investigation and solutions to other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

More Investigations

©1997-2024 WWW.TRANSUM.ORG