### Written by Bryan Lee, Joanna Sands, and Patrick Xia

In Act II, some puzzles are entangled with one in the opposite dimension. The two puzzles each have their own theme, core mechanic, answer, and solution, but each requires some information or action from the other in order to solve. This puzzle is entangled with Menagerial Problems.

Video Summary: The puzzle is a solution video of a logic puzzle called “Pumpkin Patch.” In it, the speaker starts with a Sudoku grid with five numbers, which are deemed useless. Then, he walks through a solution of “Pumpkin Patch,” shading in regions of the grid and coloring them in. Throughout the solve, he cites justification for filling in regions and also backtracks from dead ends or uses some space as scratchwork. By the end of the video, the “Pumpkin Patch” logic puzzle is solved.

In this puzzle, a solution for a hypothetical “Pumpkin Patch” puzzle is presented. Initially, it is a 9x9 Sudoku grid with five given numbers, but the number 4 appears twice in the upper-right box, so it can’t be a Sudoku. Furthermore, the speaker says we should ignore the numbers. We quickly realize that the eponymous “Pumpkin Patch” logic puzzle doesn’t actually make any sense - the explanation of the solve revolves around Halloween objects that never show up. At the end of the video, the speaker asks whether we “followed a mouse into dead ends.” In the hypothetical solution, the speaker hits “dead ends” and is forced to backtrack. We can follow the movement of the mouse for each of them to read the message: PLACE ANIMALS.

This references the animals in Menagerial Problems. In that puzzle, animals are presented in a row with colored backgrounds. Those colors match the colors in the “solved” version of “Pumpkin Patch”. Assuming the background color of the cage must match that of the region we place it in, and that all animals must be horizontally or vertically adjacent, we can place a few cages immediately. There are several clues pointing to what we should do next: the fact that there are 9 animals, the 9x9 Sudoku grid, and the reference(s) to the Sudoku-solving YouTube channel, Cracking the Cryptic.

Using each of the 9 animals as unique elements, as well as standard Sudoku rules, we can uniquely place these animals into the grid and solve the Sudoku. In this solution, we arbitrarily use the following mapping between the numbers 1-9 and the 9 animals referred to in Menagerial Problems:

AnimalAssigned number
Zebra1
Alpaca2
Leopard3
Wolf4
Chameleon5
Snail6
Goat7
Elephant8
Peacock9

A full logical solve path can be found in the appendix. After placing all the cages, the Sudoku grid looks like this:

This is the finished solution to the Sudoku.

Or, using animals instead of numbers:

Image courtesy of team_underscore

In the video, there were unused numbers from the very beginning. Using those numbers to index into the animal in the corresponding cell in the solved Sudoku results in the answer WREAK.

AnimalOriginal NumberLetter
WOLF1W
ZEBRA4R
LEOPARD2E
ALPACA4A
PEACOCK7K

#### Author's Notes

Along with Menagerial Problems, this was designed to be one half of the first pair of entangled puzzles that solvers saw. As such, we tried to include clear signs that the two were paired (through the visual use of colors, cluephrases, and matching first letters of objects and animals).

The theming behind the puzzles was inspired by the physics phenomenon "spooky action at a distance" -- the pumpkin patch represented "spooky action", while the word problems revolved around different units including "distance". We even considered splitting up the phrase and putting it into the flavortext, but ultimately decided against it for a cleaner presentation.

We had to re-record the video numerous times throughout testsolving and splice many, many takes together. These changes were precipitated by a continually changing cluephrase and color scheme (first for colorblindness, and then to avoid conflating them with resistor colors). We ended up using a subset of the colors suggested by Sasha Trubetskoy.

Lastly, a huge shout-out to Cracking the Cryptic, the YouTube channel that inspired this puzzle’s presentation, and Sven Neumann for the underlying webapp we used to record the video.