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Every Maundy Thursday, the reigning monarch distributes 'Maundy money' to equal numbers of men and women.
One year at Newcastle 64 men and 64 women each received 64p, one penny for each year of the Queen's life.
Written as a power of 2, what was the total amount distributed in pence?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
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.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?