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.

• was the flip horizontal or vertical? – JMP Dec 29 '18 at 18:19
• @JonMarkPerry Horizontal. I had a feeling someone would ask that. :) – Franklin Pezzuti Dyer Dec 29 '18 at 18:19
• yeah, coz the paper itself doesn't look flipped.,. – JMP Dec 29 '18 at 18:20
• NOTE: Minor tweak made to first image. – Franklin Pezzuti Dyer Dec 29 '18 at 18:26
• Meaning the axis of rotation is horizontal? – Dr Xorile Dec 29 '18 at 19:10

The puzzle is a

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.

• Interesting, but not the solution I had in mind. I have added a hint to the question that gives a little bit more information. – Franklin Pezzuti Dyer Dec 29 '18 at 19:56