Sorting Machine

We are presented with a pyramid of labeled pegs, with boxes and fire at the bottom, as well as a list of inputs and outputs. This resembles a Plinko machine, and we deduce the inputs are placed at the top peg and fall to their outputs, going left, right, or getting stuck at each peg. By swapping the pegs, we can change where each input falls. However, we notice every peg is consistent - that is, any configuration of pegs yields the same outputs. This leads us to the conclusion that each peg follows a discrete rule for where to send an input.

By quickly determining which pegs are stuck (D/G), and moving them to the side on the 2nd and 3rd rows, we can create a system to test what words go to the left, and which go to the right. Using this info, we can determine what rule each peg uses to sort words.

Additionally, we are given four example inputs and paths towards their respective outputs.

We notice each example input falls into a different output box (not fire), and that each input is closely related to a playing card suit: BRILLIANT - Diamond, EXCAVATE - Spade, IRON - Club, ORGAN - Heart. The flavor text also hints at this, and looking at the rest of the inputs, they also seem related to the suits. Thus we assign a suit to each box according to the examples: Box 1 = Diamond, Box 2 = Heart, Box 3 = Club, Box 4 = Spade.

We can now use these suit assignments to define a target output box for each input. We can then use the inputs and examples to figure out two things: the rule that each peg follows to send an input left or right (or get stuck), and the placement of the pegs such that each input falls into its target output box. The logic for this can be found in the Appendix, and these are the resulting peg rules and placements:

Then, given this final configuration, we keep track of the path taken by each input. Using a 0 for false/left and a 1 for true/right, the path of each input maps to a five-digit binary number, which we can convert to a letter in the canonical manner.

Reading in the order of inputs, we get the clue phrase BELIEVED BY MANY BUT OF DUBIOUS ORIGIN. This is the definition for our answer, APOCRYPHAL.

Appendix

Looking through our list of pegs, and our given sorting examples, we can quickly determine that only peg N can sort them correctly as the first peg hit (R1C1), which we can then fix in place. Similarly, note that all of the examples also hit the middle peg (R3C2), and only peg E will sort the given words correctly, so we can start by placing those 2 pegs.

For the first peg in row 2 (R2C1), we are looking to get both BRILLIANT, EXCAVATE, and IRON to go right, narrowing down our choices to pegs B, J, and K. However, if BALLPARK reaches peg E, it will go to the right and be unable to reach Box 1. Thus, the only one of these 3 pegs that makes BALLPARK go to the left is K.

BREAST follows the path N -> K -> E down, and ends to the right of it. Since it needs to end in Box 2, R4C3 must send it to the left, as well as sending EXCAVATE and IRON to the right. Among our remaining pegs, only B satisfies this condition, so we can place that there.

Similarly, NIGHT follows N -> K ending to the left, and must end in box 3. Therefore, R3C1, R4C2, and R5C3 must all send NIGHT to the right. We also know that R5C3 must send BREAST to the left from above, and ORGAN to the left. The only peg that satisfies all 3 of these constraints is C, which we place here.

Now we have a lot of constraints on R4C2. BRILLIANT must go to the left, ORGAN to the right. In addition, PALPITATION and VALVE follow a path down to R4C2, and sending those to the right would have C push them into box 3, so they must also go to the left. The only peg that satisfies this is I, which we can place now.

For R5C4, we need IRON to go left and EXCAVATE to go right. In addition, SHOVEL, TROWEL, and GARDEN (all Box 4 words) also need to go right on this peg. For our remaining pegs, the only one that satisfies these constraints is O.

If RINGS reaches peg I, it will bounce to the right, and be unable to reach box 1. Therefore, RINGS goes left on R3C1, since NIGHT goes right on R3C1, the only peg that satisfies these rules is L.

BALLPARK now ends up on R5C2 and must go left, while VALVE must go right, forcing that to be peg M.

RINGS will reach R4C1. If it goes to the right and reaches M, it will reach Box 2 which is incorrect, and so it must go to R5C1. Likewise, GIG reaches R2C2. If GIG goes to the left, it'll bounce repeatedly to Box 1, so it must go to the right. There's only 2 pegs left unused now, R4C4 and R5C5, so these must be our stuck pegs.

The only peg that bounces RINGS to the right now is J (the all right peg), so that must go in R5C1. Afterwards, only peg F bounces GIG to the right, so that must go in R2C2.

Finally, if we put peg A in R3C3, GLEE would get stuck on D, so that must be H (the all left peg), and A goes in R4C1, finishing the puzzle.