/sci/ - Science & Math

>>12664278
Attempt #2: 8x8. [math]K_8[/math] has 28 edges. Divide by 8; we want... 3.5 edges per row. That's impossible. But we can have 7 rows of 3 and 1 rows of 4 for a total of (3*7)+6=27 edges.
... Wait.
Shit. There's nowhere to put one last cell in the last row. Either my algorithm didn't work, or we need to distribute cells to rows differently.
I'm open to suggestions on this one.
>>12664326
Edges in a graph.
https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
In this case, an edge is just a pair of columns containing filled cells in a row. When you convert a row in the grid to a clique in [math]K_n[/math], a pair of filled cells becomes an edge in the clique. If two of those cliques share an edge, it means that the corresponding rows have filled cells in the same columns, and that's bad.