A beautiful problem from a Hungarian competition
Discrete Mathematics
Level
4
We need to fill each cell in a \(6\times6\) grid with a distinct integer from 1 to 36. There are two rules:
- Every pair of consecutive numbers are in adjacent cells that share an edge.
- Any two cells containing a multiple of 4 cannot share an edge nor a vertex.
Over all valid configurations, how many of the 36 cells could contain the number \(36?\)
\(\)
Note: Below is a \(3\times 3\) grid adhering to the rules above.
by
Áron Bán-Szabó