# The Legend

### with production by Brian Shimanuki, Jacqui Fashimpaur, Jordan Bunker, Lindsay Oliver, Mona Wang, Moor Xu, and Sylvia Jin

This is a metapuzzle in the Wyrmhole round.

The use of "linking" in the flavortext and the puzzle title suggest using The Legend of Zelda, and the given diagram indicates we should assemble the 27 given triangles into a larger shape with an N, L, and Z at the three corners.

A common motif in The Legend of Zelda is the Triforce, made of 3 golden triangles. From 27 triangles, we could create 9 Triforces. Continuing this idea, the 9 Triforces could be combined into 3 Tritriforces, which could turn into 1 Tritritriforce. Or more commonly, the 27 triangles can be arranged according to the Sierpinski triangle fractal.

If we count the letters on the given triangles, then count the letters in our feeders, we find that every letter of our feeder exists on the triangles. Furthermore, some triangles contain subsequences of our feeders (this may be easiest to notice from the EIJ triangle, which is part of BEIJING TIGERS). So, this suggests that we should place the triangles such that we can find all feeders as paths on the resulting shape.

Once we understand all these steps, the puzzle turns into a logic puzzle. We can provisionally assign triangles to feeders based on uniqueness of certain letters or 2-letter and 3-letter substrings. This is possible because when we are in the middle of a path, we must enter and exit a triangle at 2 different points. Said triangle must have 2 or 3 matching letters with the feeder answer.

Here is a walkthrough of assigning triangles to CARBON SINK, as an example.

• There is only one K among all triangles, on the EKT triangle. There is no N in EKT, so CARBON SINK must end on the K and be split like CARBONSIN(K).
• The previous triangle must overlap either IN or SIN. There is no triangle with SIN, so it must be just IN, giving CARBONS(IN)(K).
• The one before IN must be NS or ONS. There is an ONS triangle, so it could be either.
• Jumping ahead, consider the B in CARBON SINK. The triangle with the B must have one of ARB, RBO, BON, RB, or BO. Looking at the 27 triangles, the only possiblity is BO. This gives CAR(BO)NS(IN)(K).
• Now using ONS after BO is impossible, so it must be CAR(BO)(NS)(IN)(K).
• Finally, there is no CAR triangle, so CAR must be split across 2 triangles, giving (C)(AR)(BO)(NS)(IN)(K).

We can use similar logic on the other feeders. Not all feeders can be fully split in this way, but we can reduce the possibilities enough to check the remaining options by hand. Once the feeders are split into a chain of triangles, we should try placing them into the Sierpinski shape. This is unconstrained on its own, since the chain can bend or not at every corner, but when all chains are considered as a whole, there is only one way to place them into the grid that's consistent with the given corners and Sierpinski triangle. This is easiest done via guess-and-check, and some good start points are the LTR triangle in the corner or the EKT triangle that must be shared between GEOM(ET)RIC SNOW and CARBON SIN(K).

The only corners with matching letters are the bottoms of the 9 smaller Triforces. Reading these letters in order, we get the answer INCEPTION.

## Authors' Notes

The triangle theming within all the Wyrmhole metas originates from this puzzle. We wanted a fractal-y starting meta as a teaser for the rest of the round, and after a proof of concept for this puzzle tested successfully, we backported the triangle theming to all other meta drafts and chose TRIFORCE as the answer to close the loop in Wyrmhole. This did arguably break The Error That Can't Be Named, but we wanted to make the triangle motif as strong as possible for that answer.