Solution to Escape From Life — MIT Mystery Hunt 2021

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Answer: FLYER

by Evan Chen

We start by identifying all the images and filling in the blanks. As hinted by the title, these are all various patterns in Conway's Game of Life. Most of them are considered common patterns and listed on, e.g. bottom of the Catagolue. (The one exception is the rare snake with feather.)

Word	Index	Letter
Pond	4	D
Mango	5	O
Loaf	4	F
Scorpion	3	O
Tub	2	U
Eater 1	5	R
Long boat	4	G
Block	2	L
Snake with feather	7	I
Toad	4	D
Beehive	2	E
Pulsar	6	R
Shillelagh	1	S
Half-bakery	10	Y
Blinker	4	N
Boat	4	T
Ship	2	H
Ship-tie	7	E
Moose antlers	4	S
Paperclip	8	I
Integral sign	9	S

This gives us the cluephrase DO FOUR GLIDER SYNTHESIS. This means we should fill in the red squares in the images at the bottom to get gliders and see what hapens when they collide. The two corner cells of the glider are filled in, and as it turns out, there is exactly one way to orient the glider so that those corner squares match up and the glider flies towards the center of the pattern.

Upon running the simulator one finds that each collision generates an ash pattern, and (as hinted again by the title), two outgoing gliders or spaceships escaping from the debris. The directions in which they escape give semaphore letters. The images at the bottom are sorted in alphabetical order.

Starting picture	Resulting ash	Escaping gliders	Semaphore letter
		NE and S	E
		NE and S	E
		NE and S	E
		NW and SW	I
		NW and SW	I
		NW and SW	I
		NE and SW	L
		NE and SW	L
		NE and SW	L
		SE and SW	N
		SE and W	S
		SE and W	S
		N and NW	T
		E and NE	W
		NE and SE	X
		E and NW	Y

The images in the final six-by-six grid are representations of the ashes using the cartoons we identified previously. Pairing the ashes with the corresponding cartoon images yields the following grid:

Using the small images as additional clues for the words, the grid can then be filled as a symmetric word square:

The final step is to run the grid one more step, as indicated by the only piece of unused information, the t+1 in the lower-left corner. So running the grey cells one more generation gives the following grid:

The letters in the living cells inside the grid now spell FLYER, the final answer.

Author’s Notes

Conway's Game of Life occurs reasonably often on Mystery Hunt puzzles, so when I set out to write a puzzle using it, I was insistent on using a puzzle that would take advantage of the Catogolue. As far as I was concerned, a mapping of various still lifes to canonical names (which could then be represented by images) was a puzzle gold mine.

The idea I liked the most was having escaping ships signal semaphore letters, and that was the only part of the puzzle that was more or less unchanged through the many different versions of the puzzle.

It was a challenge to find syntheses that would produce some of the rarer shapes. I left my gaming PC running for a few days running Life simulations with various inputs to try and see which ones would yield exactly two spaceships. It turns out that it's reasonable to get two diagonal gliders, it's harder but doable to get one orthogonal and one diagonal glider, but obtaining two orthogonal gliders was nigh impossible. This led to a lot of various awkward extraction mechanisms which were scrapped one after another until we settled on the word square.

Still-lifes that I managed to synthesize but couldn't squeeze into the puzzle included cis-shillelagh, trans-boat with tail, boat tie ship, hat, tub with tail, big S, bi-pond, very long ship.

The suggestion for the title "Escape from Life" is due to Patrick Yang and Jon Schneider (the original title for the proposal was "Synthesis").