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.