Silph Puzzle Hunt 2021/Δ

Δ (AKA 'Delta') is an early puzzle in Round 2 of the 2021 Silph Puzzle Hunt. Solvers are presented with rows of clues inside of boxes of various sizes, with an enumeration given at the end of each row. One of the rows oddly has quotation marks and a comma between the boxes, implying perhaps each box will reduce to an English word or phrase and is meant to be read.

Solve Path
After solving all of the clues in a particular box, solvers may notice something peculiar about the answers they filled in. The answers seem to come from a small pool of letters. This fact will become more apparent as more boxes are correctly filled in. Upon further inspection, solvers may notice that within each box, the number of occurrences of a specific letter is unique. This fact is particularly apparent the smaller boxes, such as the box with one clue, Hockey legend Bobby which clues to ORR. This fact clues solvers to arrange the letters in each box into a triangle, as hinted by the title.

Alternatively, this same fact can be arrived at by summing the enumerations of each box, and the final enumerations at the end of each row, and noticing that these numbers are all part of a particular sequence known as the Triangle Numbers.

Reading the triangles made from each box, from top-to-bottom, yields a word. When read with other boxes in the same row, a crossword-style clue is formed. The answer lengths of these clues is given by the enumeration at the end of each row. The first row, for example, solves to:

Z       M        B   E E      A A      A A  R R R    P P P    N N N    O O O O  S S S S  D D D D

Combined with the quotation marks and comma presented in the puzzle, it reads "Zero", "Maps" Band (4,4,5), which clues YEAH YEAH YEAHS.

After solving all of these new clues, solvers are meant to repeat the step they did at the beginning, and make a triangle out of the new letter bank. There are 66 letters from the row clues, so solvers need to make a triangle of height 11, and read from top-to-bottom. Each letter is still used a unique number of times, allowing solvers to approximate the construction of the triangle even without all of the answers to the rows.

Reading top-to-bottom on the new large triangle yields the final answer.