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Street Sequences

Stage: 1 and 2 Challenge Level: Challenge Level:1

Nick, Harish and Jonathan from Mason Middle School investigated these street numbers in groups of three. They wrote:

When you add the first number on the top and the third number on the bottom they equal seven.
Also the third number on the top and the first number on the bottom equal seven. Finally, the second number on the top and the second number on the bottom also equal 7.
If you add the diagonals two away (I think this means the six houses which have numbers 5, 7, 9 and 6, 8 10) they become 15. The sum is 8 more than before.

Ella from the British School in Amsterdam did a similar thing and said that the diagonal totals are the same number.

I wonder whether anyone can explain why?

We'd love to hear about other things you investigate. Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send a summary of your children's work.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.