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Investigate

$$ 1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$$

and

$$ 2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$$

for different values of $n$.

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What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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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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