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# Neighbourly Addition

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Age 7 to 14

Challenge Level

As I walked down the street this morning, I noticed that all of my neighbours' house numbers were odd!

I added three house numbers together as I walked past: 7 + 9 + 11 = 27

Further down the road, I passed some bigger numbers. I added another set of three neighbouring house numbers: 15+17+19 = 51

**Can you find some other totals I could make, by adding together the house numbers of three (odd) next-door-neighbours?**

Once you've found a few totals, here are some questions you might like to explore:

Is there anything special about all the totals?

Is there a quick way to work out the total?

Can you predict what would happen if I walked down the other side of the street instead (where all the houses have even numbers)?

Are there any patterns if I add together four house numbers instead of just three?

Or five house numbers?

Or...

Can you explain and justify the patterns you have noticed?

*This task was used in a student webinar led by members of the NRICH team. You might like to watch the video footage of the webinar.*