### Games Interactive 2: Thinking About Battleships

I find that there are two distinct modes of thought involved in solving Battleships puzzles. It’s not quite the “logic vs intuition” thing again, though.

On the one hand, you have the same sort of approach as Paint by Numbers puzzles: proving things about the grid. You have certain constraints, including puzzle-specific ones like “this row has exactly three occupied spaces in it” and general ones like “there is exactly one set of four consecutive occupied spaces”, and from these constraints you construct chains of reasoning about what must be in specific spaces. “There are two three-tile long ships and only three places where they can fit. So at least one of them must be in one of these two places, both of which border on this square. Therefore, this square is unoccupied.” You then mark the square as unoccupied, and start using that as a constraint in further proofs.

On the other hand, you can also think of it as an assembly puzzle, like pentominos or tangrams. You have ten pieces of varying length, and you have to put them together into a shape that fits certain constraints. True, most assembly puzzles use a target shape where the pieces touch each other, and that’s specifically forbidden here, but that doesn’t really make much difference. You’re still thinking about it in terms of moving pieces around. There’s typically a very limited set of places where the four-long ship can go, so you try it out in one of those places, and when you see that it prevents the rest of the pieces from fitting in nicely, you move it somewhere else. This is really equivalent to reasoning from trial-and-error, but I find that conceptualizing it as moving pieces around makes it a lot easier. Sometimes I’ll mark in all the pieces in an way that doesn’t fit the numbers, because it helps me to see how to fix the problem by moving something.

Usually my trajectory through a puzzle starts with the former approach, and switches to the latter when progress fizzles out. In some puzzles this happens very quickly. Notably, the UI discourages the assembly model. I can think about it in terms of moving pieces around, but I can’t actually remove an entire ship from one place and put it somewhere else as an action. The only form of interaction is marking and erasing individual tiles, which fits better with the other approach. This sways how I want to solve the puzzle. I can’t blame *Games Interactive* for this, though. The same applies even more strongly to the print version.