# Torus Flow Free

Rules: this is a flow free warp puzzle with a 9x9 grid. connect the respective letters together with lines that travel orthogonally through the centers of grid cells.

additionally, the sides of the puzzle and the center column of the puzzle are warps; you can enter from one side and exit the other. for example, this is a valid path (the path being the highlighted cells).

Explanation:

I think the main question is, which color will go through the center column?

There are 4 different colors, so there are 4 possibilities. The main reason you'll want to use this gap, is that another color could go around this color. This gets the second color 'at the other side'

Note that both B and C are adjacent to the cells connecting the center column gaps.

So if B or C is using this center gap, you can't use the importance of this center gap.
The next thing to notice is the combination A - B - A at the right of the puzzle. This B is trapped between the 2 A's, So something has to happen if B wants to escape to the other B. On the other hand, the one D is completely free, so the D probably doesn't have to use the center gap. If now we know the A is going through the gap, we would have the following. (let's immediately avoid the D's, to make it easier to connect the D's later on)

This now forces the below C to the right, and that makes there's only one way on how the A is going through the gap:

And this let us see how the B's and the D's should escape, and the final answer reveals us:

• brilliant! that was my intended logic path. it's pretty difficult (i sent this in the thinky games discord a while ago and nobody managed it). good job! :) Commented May 26 at 12:47
• It was pretty hard indeed, but that's why I really liked this puzzle. Explaining everything that went through my head even harder xD Commented May 26 at 12:54

As in Lezzup's answer (but more formally),

Which line goes through the central warp?
Notice that if neither A nor B use the warp, then A's and B's paths form loops that separate each other:

Can B use the warp?
No, because if the top B uses the bottom warp (red), then some loop isolates A, and if the top B uses the top warp (blue), then A and C are forced to separate each other since neither can loop around the other.

Therefore, A warps. If the bottom A uses the bottom warp, C is isolated, so the top A uses the bottom warp, and we get this configuration, so as not to isolate D:

Now if A claims the space along the bottom right, it will isolate C in the process of rejoining one of its endpoints, so B must claim it instead. At this point, simple connectivity is enough to force the remainder of the solution:

• yep! i just wanted to showcase the topology that you can implement in flow free with warps. btw i'm trying to make something similar but with no walls at all and oh god it is difficult lmao. i guess no more flow free puzzles from me for a long time. Commented May 27 at 14:27