@Alireza: 9: I didn't try to find a formula, but I made the grid in a spreadsheet, and for each cell, I calculated if the line would pass through that cell.
21: I thought about each group of even A's as a single unit, and thought about how many ways that group of A's could be slotted among the B's. The simplest version of this is the following. You have 2 A's and 9 B's. Treat the 2 A's as a single unit that can't be divided. How many ways can you slot that unit among the B's? Now do that for every possible configuration of even groups of A's. It seems like it'd be a ton of calculation, but it ends up being "only" like 30 cases or something.
21: I thought about each group of even A's as a single unit, and thought about how many ways that group of A's could be slotted among the B's. The simplest version of this is the following. You have 2 A's and 9 B's. Treat the 2 A's as a single unit that can't be divided. How many ways can you slot that unit among the B's? Now do that for every possible configuration of even groups of A's. It seems like it'd be a ton of calculation, but it ends up being "only" like 30 cases or something.
on /blog/120