## A nifty partition of 1..16

Courtesy of Phil Harvey’s Puzzle « Programming Praxis, I discovered that the numbers from 1..16 can be partitioned into two 8 element sets, with these nifty identities!

2+3+5+8+9+12+14+15 == 1+4+6+7+10+11+13+16

2^{2}+3^{2}+5^{2}+8^{2}+9^{2}+12^{2}+14^{2}+15^{2} == 1^{2}+4^{2}+6^{2}+7^{2}+10^{2}+11^{2}+13^{2}+16^{2}

2^{3}+3^{3}+5^{3}+8^{3}+9^{3}+12^{3}+14^{3}+15^{3} == 1^{3}+4^{3}+6^{3}+7^{3}+10^{3}+11^{3}+13^{3}+16^{3}

There has to be a good way to use this to make a cool geometric puzzle as well.\

**Bonus:** Are there any other values of N such that the numbers from 1..N can be split into two sets, each of which have the same sum, sum of squares, and sum of cubes?

**Spoiler:** Yes, there are.

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