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Plates of Biscuits

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are $12$ plates of biscuits with $3$ identical biscuits on each plate.

2 plates of biscuits with three identical biscuits on each plate: Almond fingers, Bourbon, Choc chip, Digestive, Easter biscuits, Fig rolls, Jammy dodgers, Kiwi cookies, Lemon puffs.

(They are named simply to help identify them by a letter!)

Can you rearrange the biscuits on the plates so that

  1. The $3$ biscuits on each plate are all different
    and
  2. There is no plate with two biscuits the same as two biscuits on another plate?

For example, if you have one plate of 'A, D and F' then you cannot have another with both 'A and D' or 'A and F' or 'D and F'.


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.