# Sunday Times Teaser 2777 – Summing Up 2015

*by Richard England*

#### Published: 13 December 2015 (link)

I asked Harry and Tom to write down three numbers that between them used nine different digits and which added to 2015. They each succeeded and one of Harry’s three numbers was the same as one of Tom’s. I noticed that Harry’s three numbers included a perfect square and Tom’s included a higher perfect square.

What were those two squares?

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Here’s my solution (using some minor routines from the

enigma.pylibrary for neatness).I note that you have disambiguated the question to require each of the digits to be used only once. Without this condition there are several solutions (if you remove the additional condition in my code you will see them).

A stronger condition would be to require each of the numbers to only have three digits. Even with this stronger condition there would be multiple solutions for 2016, but for 2017 there is a unique solution.