by Ben Monreal
Answer: EMBOLI
Problem: Holi Town/​Patriots’ Day Town

You are given a body-shaped grid of four colors and some indicators that there is one way in and six ways out. Although there are 24 unique orderings of four symbols (say ABCD) there are only six unique loop orderings: ABCD, ABDC, ACBD, ACDB, ADBC, ADCB. As per the flavortext, you need to follow ALL of the doctor’s orders—and indeed the six differently-worded prescriptions illustrate this. Pick an order, start at the “in” arrow, and follow a path that hits the colors in that order. Some edges in the grid are blocked by white ovals, which your paths may not cross. Each cycle should lead to one of the exit arrows, where there is a little equation. Count the number N of squares in your path. In order from head to toe, you have paths of lengths 54, 76, 79, 79, 80, 83. Plug those into the equations and you’ll get 1, 19, 3, 9, 9 and an encircled (14), which via the obvious A=1, B=2 translation spells ASCII (N). Note that the N’s in the equations are also circled! Go back to the cell counts N and interpret them as ASCII. Now it spells 6LOOPS.

Somewhere in the grid, not connected to the arrows, are six loops—one clockwise loop for each cyclic permutation. Find them.

(Some hints as to search strategy: first, it’s clear that an ABCD loop cannot have intersected either the ABCD or the ADCB path, or you’d have found it already. Second, look for those little rips or bubbles—if they’re blocking something that your previous route-finding didn’t need blocked, that’s a good place to start; every loop has at least one such bubble along it. There a lots of those bubbles in the left arm to steer you towards the smallest of the loops.)

A loop has to be a whole number of cycles—you may have noticed that the equations were written, not in their simplest form, but in a form with an (N/4) term that counted 4-cycles—so you have previously seen that we can count cycles and interpret the results with A=1. Taking the clockwise* permutations in the head-toe order again, you found loops of 5, 13, 2, 15, 12, and 9 cycles, which translated with A=1, spell EMBOLI—which is the answer to the puzzle, a decent interpretation of all those path-interrupting bubbles, AND a good reason to be getting all that heparin.

*(If you followed the loops counterclockwise, head-to-toe sorting of the cycles spells IOLMBE and I hope that’ll prompt you to try the other sense.)

Color as drawnSequenceMaze length NEquation ℞“ASCII N”loop cycle count
Red green-purple-orange-yellow 541 = “A” 6 5 = “E”
Magenta green-purple-yellow-orange 7619 = “S” L 13 = “M”
Black green-orange-purple-yellow 793 = “C” O 2 = “B”
Blue green-orange-yellow-purple 799 = “I” O 15 = “O”
Brown green-yellow-purple-orange 809 = “I” P 12 = “L”
Cyan green-yellow-orange-purple 8314 = “(N)” S 9 = “I”