brainwagon

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
2²+3²+5²+8²+9²+12²+14²+15² == 1²+4²+6²+7²+10²+11²+13²+16²
2³+3³+5³+8³+9³+12³+14³+15³ == 1³+4³+6³+7³+10³+11³+13³+16³

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.