Academic Snake Pit

Question

One day, you get lost in the corridors of your new school and accidentally wander into a pit full of venomous snakes. Unfortunately, the pit is deep and you have hurt your leg in the fall, so there is no climbing out. Fortunately, since you're in a school, all of the snakes are educated and would much rather force you to do a puzzle than eat you.

The snakes give you the following puzzle on a crumpled sheet of paper, under threat of death by poison should you fail to solve it. The front of the paper looks like this:

If you flip the paper over, the back looks like this:

Better not waste time! Although these snakes are academic, it certainly isn't above them to kill and eat a human.

HINT:

The tape is there for a reason.

Answer 1

The puzzle is a

slitherlink

but played on a

torus board, i.e. one where the edges wrap around.

From the snake on the back you can see that the left/right edges map exactly onto one another (regardless of how the rectangular paper is turned over, the snake shows short sides match). The top/bottom edges however don't map directly, but are slightly shifted. There are two ways they could connect, because there are two grid points directly on the top/bottom edges. After filling in the walls of the lower 3 square, the partial square below it has two walls. It therefore becomes clear that this square cannot be the 1 in the top row. The square below the bottom 3 must therefore be the 3 in the top row.

Once this mapping is known, it is just a matter of solving the slitherlink puzzle. It is straightforward, but slightly confusing due to the wrapping. Here is the solution, copied a few times to show the edge mapping.