Public Access

Solution to The Colour Out of Space

by Tracy Cobbs

Solvers are presented with three cryptarithms. (A cryptarithm, also known as verbal arithmetic or alphametic, is a type of puzzle in which letters have been substituted for numbers and which is solved by pairing digits with letters to produce an arithmetically correct answer.) Although by default most cryptarithms use decimal (base 10) and a single letter-to-digit key, these use duodecimal (base 12) and two keys. Double-key cryptarithms are often presented with one key using uppercase and the other using lowercase, but for thematic reasons these use two different colors in each cryptarithm for a total of six different colors.

Here are the solutions and keys for each cryptarithm. Online calculator: Simple math in any numeral system (planetcalc.com) is a good resource for checking the math, or you may have your own preferred duodecimal calculator.

``````
LURCH
35147
HORRID IRRATIONAL
2B4437 A11B6A89B3
TMPAMW
8A10A9
RLGIORO
130A818
PHTWWNO
128995B
CGIHNN
40A799
HORRID
2B4437
RRTLTFA
116362B
OWNNHR
B95524
ROIRGHL
18A1073
PTDEEPP
1876611
FTTTF
26662
``````
 F R A N T I C G H O U L 2 1 B 9 6 A 4 0 7 8 5 3
 W E I R D P H A N T O M 9 6 3 4 7 1 2 0 5 8 B A
``````
WITCH
247A9
MOURN SORROWFUL
2A783 6A88A4079
SHEIA
59346
TTEWWW
115444
DAAHN
B6690
TOLUWF
1A9740
UBWSHH
182599
MUTSNU
271637
WICICA
24A4A6
MNTETL
231519
WUDHWE
21B923
TTUAS
117B6
``````
 A W F U L M O N S T E R B 4 0 7 9 2 A 3 6 1 5 8
 D U N W I C H B E A S T B 1 0 2 4 A 9 8 3 6 5 7
``````
MOLDY
4835B
OLDONES NECRONOMICON
8358A16 32A793916A93
AHENYMST
291AB460
TLLOHNMI
5889B316
DSLHNHTT
5639A900
ETDDIMIC
2500616A
ATNDASMS
20A52646
AMRNREAO
41737249
LDDMOAGS
35548276
LMCCHONN
81AAB933
GGALELMS
77231346
ILRCTCO
687A5A9``````
 G H A S T L Y D E M O N 7 9 2 6 0 3 B 5 1 4 8 A
 E L D R I T C H M O A N 2 8 0 7 6 5 A B 1 9 4 3

For the purpose of this walkthrough, I’ll consolidate all the keys into a single table to help with substitutions in the next step:

 0 1 2 3 4 5 6 7 8 9 A B G R F L C U T H O N I A A P H I R N E D T W M O F T M N W E S U R L O A N U W E I S A T B H C D T E A L M D S G O H N Y D M E N A T I R L O C H

The final two lines of the puzzle give the extraction. Substituting digits for letters of the given colors yields the next set of divisions:

``12 3095A    1099 5409    7 9B19    2702 A408``

Calculating the solutions to those (still in duodecimal) yields 2765, 5, 1503, and 4.

Converting those numbers back to letters using the given colors of the question marks yields WHIT, E, TUNI, and C.

The final answer is WHITE TUNIC.

Author's Note

I knew early on that I wanted to write a cryptarithm puzzle for this Hunt. It’s a type of puzzle I’ve had plenty of experience with, as the editor and co-author of A Cryptarithmetic Tribute to England. (Available for free download at the link.)

There was a possibility, early in planning for this Hunt, that we might be choosing a Hitchhiker’s Guide to the Galaxy theme for the 42nd MITMH. Even after Bookspace became the theme, there was still a Sci-fi round where H2G2 references would fit. At that point I considered having all the cryptarithms yield the quotient 42. There was a feeder answer of “NO CONFIDENCE” for a Sci-fi meta candidate (one which eventually didn’t make the cut) and I thought I could tie that in nicely to Marvin the Paranoid Android. When the chosen Sci-fi meta didn’t seem to have any feeder answers that fit with the H2G2 theming, I made the switch to Horror, and went whole hog with the Lovecraft theming.

The editorial recommendation Foggy Brume gave after my first draft was to take a second look at the extraction. Boy, am I glad he suggested that! Discovering that I could use the iconic Lovecraftian phrase from “The Call of Cthulhu” in a way that fit with the mechanics of this puzzle and yielded a string of the same length as the assigned answer was really something special.

If you enjoyed this puzzle, I would highly recommend joining the American Cryptogram Association. Their bimonthly journal contains 16 cryptarithms in every issue. Since back issues all the way back to the 1930s are available online to members (as PDFs), there are thousands of cryptarithms for you to catch up on.