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Try to list all the possible combinations for set $A$.
Try to be systematic so you don't miss any combination.
 
How can I end up with an even total?
By adding two even numbers? An even and an odd? Two odds?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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