Create a 5x5 grid.
A1 A2 a3 a4 a5 B1 B2 b3 b4 b5 c1 c2 c3 c4 c5 d1 d2 d3 d4 d5 e1 e2 e3 e4 e5
Seed A1, A2, B1 and B2 with numbers that allow the grid to be completed with following criteria:
- Except in the first to columns, every cell must be the modulo of the 2 cells left to it.
Except in the first two rows, every cell must be the modulo of the 2 cells above it.
No more than one cell is allowed to be 0.
Numbers may repeat in the grid
- c3 = a3%b3 = c1%c2
- e5 = e3%e4 = c5%d5
The solution with the lowest sum of initial numbers wins.
Can you choose 4 different numbers to start with? (That adds a hell of complexity :)