A Dark Tor Riddle Faithful

The Dark Tor Riddle is an open, interconnected mathematical construct that means absolutely nothing at all to the players. It should never be used as a competitive mechanic in any way. It is truly a mathematical mystery with no way to win.

Anyone that knows anything about the game knows the tor means eternal pain, but it does not mean the tor itself is eternal, for it has a number of intermediate versions, which may or may not be able to be won, as players contend with them for any given turn. This answer to the problem of how the tor is broken is that it is not broken, rather, it is something in the engine that is broken.

What the tor is

A tor is a pseudo-randomized form of a knot with two legs. It may be drawn with the colors red, black, or brown, and may either have two or four legs. The tor is created by starting with two centers in a circle and then connecting points equidistant from both centers. The tor construction is such that, at any point during a game, the two circles each may be stretched, rotated, or compressed.

Is it a tor?

No. It is a knot with several knotted- together configurations, whether it is a tor itself or a twisted version of one. One such twist is a looped tor.

Example:

Torus (2 twisted legs x 2 legs)
This knot allows for all the intermediate steps. The two centers of the tor are shown above.
The game can now be drawn.

The game needs four colors to choose a tor. Any two colors could be used. The colors red and green are equally equally likely and may have only a single leg. The colors yellow and blue indicate that two legs are broken, and could be used once each.

The game ends if someone reaches a center point. However, it may be played indefinitely. A game may be played until either the center or a newly linked center reaches the next turn. After all the steps are completed, the game ends. Once the linkages have been made, it is a matter of finding a middle point until the tor has been made.

The game may have the number of leaves determined based on the number of colors and how many arms are necessary and tied together to make an armadillo.