Unit 12 · Multi-Step Conditional Reasoning
Gabi and Luke's Cipher — Ambiguity Problem
Lesson 8 of 30
About this lesson
A substitution cipher maps 26 letters to only 10 digits — so several letters must share each digit. Gabi encodes four words. Luke decodes three with confidence. One word he can't be sure about. Why? Because its digit sequence also spells a different real word.
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Question
Gabi and Luke want to use a code to send secret messages to each other. In the code, each letter of the alphabet is represented by a one-digit number, as follows:
| A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| K | L | M | N | O | P | Q | R | S | T |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| U | V | W | X | Y | Z |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
For example, the word BELL would be written in the code as 2-5-2-2.
To test the system, Gabi writes four words in the code and sends them to Luke. Luke tries to decode them, and gets the following answers:
TOOK
DONE
HIGH
SORT
Luke is confident that he has three of these words correct, but he is unsure about the other one.
Which word is Luke unsure about?
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