## December 2018 - Solution

Every natural number can be represented as a multiplication of powers of prime numbers.

The exponents of this representation, modulo 2, can be viewed as a linear vector space.

Each “boring” cycle is a linear sub-space, and therefore it is easy to combine two sub-spaces of dimension 3 to a sub-space of dimension 6.

The interesting fact is that one can combine two sets that are *not* linear sub-space together into a linear sub-space.

Many of you found a boring solution with 2,251 solvable numbers, like [[3, 7, 11, 13], [2, 5, 14, 65]].

George Lasry, Deron Stewart, Jingran Lin, Andreas Stiller, Alper Halbutogullari and Oscar Volpatti found solutions with 2,556 solvable numbers such as: [[14, 231, 374, 34], [13, 1482, 95, 10]].

Alper Halbutogullari also found a solution with exactly 2,187 solvable numbers: [[10, 5, 13, 39], [17, 51, 7, 66]].