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Sums of Pairs

Age 11 to 16 Challenge Level:

Jo has three numbers which she adds together in pairs.

When she does this she has three different totals: $11$, $17$ and $22$

What are the three numbers Jo had to start with?

Can you describe a method that would enable you to work out the three numbers given any three totals?
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.