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.