For example,

partitioning

{3,4,5} ……………………

{2,3,4,5,6} ………………

{5,6,7,8,9,10,11} ………

{1,2,3,4,5,6,7,8}

partitioning the numbers from 1 to **12** into sets with the same square sums:

partitioning the numbers from 1 to **16** into sets with the same sums and square sums

partitioning the numbers from 1 to **20** into sets with the same square sums:

from 1 to **28**:

partitioning the numbers from 1 to **32** into sets with the same sums and square sums

(1) partition the numbers from 1 to **64** inclusive into 4 sets with the same sums and square sums

(2) partition the numbers from 1 to **256** inclusive into 4 sets with the same sums, square sums, and cube sums

(3) partition the numbers from 1 to **125** inclusive into 5 sets with the same sums and square sums

Generalize all of this.