>>16537286
>Loops are self-enclosed
Stupid way of saying that a loop divides the board into two parts, the area outside of it and the area inside of it. I should have simply called it an enclosure.
>Why?
The idea is to look at the most simple case and then show that any loop can be created by simply variating, by means of deleting one piece of the original loop (which I forgot to mention) and then adding the new loop to it (where you have to delete the one piece that overlaps with the pieces of the original loop minus the one piece you deleted. The point is that you want to go through the new curve which is the added loop minus the one overlapping piece. It's easy to show that any loop can be constructed that way because any loop can be changed in a way so as to either remove "curves" or add new ones to it such that the newly-added curves is bent towards the inside of the enclosed area. Do that finitely many times until you arrive at a 3 x 3 loop.

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can /sci/ solve this math contest problem meant for american middle schoolers?