3.3 Codes, Ciphers & Letter Substitution

3.3 Codes, Ciphers & Letter Substitution

Code questions are among the most predictable and high-scoring sections of the Kent Test 11+ Verbal Reasoning paper. They test a student's ability to recognize abstract patterns, apply consistent mathematical transformations to letters, and analyze positional structures.

1. Alphabet Position Shifts (+N, -N & Alternating Shifts)

In alphabet shift ciphers, each letter in a word is shifted forward (+) or backward (-) by a fixed number of positions in the alphabet.

Alphabet Quick Reference Table

To work efficiently, memorize the numerical positions of benchmark letters (e.g., $A=1, E=5, J=10, O=15, T=20, Y=25$) or reference the complete 1–26 grid:

Shift Patterns in 11+ Exams

1. Constant Shift (+N or -N): Every letter shifts by the same constant offset.
   • Example: $+3$ shift $\rightarrow$ $C(3) \rightarrow F(6)$, $O(15) \rightarrow R(18)$, $L(12) \rightarrow O(15)$, $D(4) \rightarrow G(7)$. COLD becomes FROG.
2. Progressive Shift: The shift increases with each letter position ($+1, +2, +3, +4$).
3. Alternating Shift: Shifts alternate between addition and subtraction ($+1, -1, +2, -2$).
4. Alphabet Wrap-Around Rules:
   • Moving forward past Z wraps back to A: $Z(+1) = A, Z(+2) = B$.
   • Moving backward past A wraps back to Z: $A(-1) = Z, A(-2) = Y$.

Worked Example: Constant +3 Shift

Question: If the word COLD is written in code as FROG, how would you write the word WARM in the same code?

• Analyze COLD $\rightarrow$ FROG:
  • $C (3) + 3 = 6 (F)$
  • $O (15) + 3 = 18 (R)$
  • $L (12) + 3 = 15 (O)$
  • $D (4) + 3 = 7 (G)$
• Apply +3 to WARM:
  • $W (23) + 3 = 26 (Z)$
  • $A (1) + 3 = 4 (D)$
  • $R (18) + 3 = 21 (U)$
  • $M (13) + 3 = 16 (P)$
• Code for WARM: ZDUP.

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2. Letter-for-Letter Cipher Substitution

In letter substitution codes, letters are mapped directly to other letters according to a fixed key. Unlike shift codes, the mapping may not follow a simple arithmetic step, but is constant across all words in that question.

Deciphering Matrix Example

Suppose you are given two example words and their codes:

• BOAT $\rightarrow$ XQZP
• TEAM $\rightarrow$ PZMR

From these two pairs, extract the exact letter-to-code mapping:

B &\rightarrow X, & O &\rightarrow Q, & A &\rightarrow Z, & T &\rightarrow P \\ T &\rightarrow P, & E &\rightarrow M, & A &\rightarrow Z, & M &\rightarrow R \end{aligned}$$ Notice that $A \rightarrow Z$ and $T \rightarrow P$ match in both words. This confirms our substitution key! > **Problem:** How would you code the word **BEAT**? > - $B \rightarrow X$ > - $E \rightarrow M$ > - $A \rightarrow Z$ > - $T \rightarrow P$ > - **Encoded Word:** **XMZP**. --- ## 3. Number-to-Letter & Arithmetic Ciphers Number-to-letter codes replace each letter with its numerical position in the alphabet ($A=1, B=2 \dots Z=26$) or a transformed number value. ### Common Variants 1. **Direct Indexing:** $C-A-T = 3-1-20$. 2. **Reverse Indexing:** $A=26, B=25 \dots Z=1$. 3. **Word Total Sum:** Summing the letter values ($CAT = 3 + 1 + 20 = 24$). ### Worked Example: Word Total Sum > **Question:** If **CAT** is coded as **24** ($3+1+20$), what is the numerical code for **DOG**? > - **Calculate DOG:** > - $D = 4$ > - $O = 15$ > - $G = 7$ > - $\text{Sum} = 4 + 15 + 7 = 26$. > - **Code for DOG:** **26**. --- ## 4. Pattern Matching Unkeyed Code Groups A classic GL Assessment VR question presents four words and four scrambled code groups, asking you to match a specific code to a target word without knowing the cipher in advance. ### Target Words: `[ BEAR , DARE , DEAR , BIRD ]` ### Code Groups: `[ 1234 , 5342 , 5234 , 1645 ]` ### Step-by-Step Pattern Extraction Matrix | Feature | Word Analysis | Code Group Matching | Resulting Match | | :--- | :--- | :--- | :--- | | **Unique Letter Test** | *BIRD* is the only word with 'I' and 'D'. | Look for unique digits. | Match *BIRD* $\leftrightarrow$ *1645* | | **Shared Ends** | *BEAR*, *DARE*, *DEAR* all end in 'R' or 'E'. | `1234`, `5342`, `5234` all end in 4 or 2. | $R=4$ or $E=4$. | | **Letter Breakdown** | *BEAR* starts with 'B'. *BIRD* starts with 'B'. | Both `1234` and `1645` start with `1`. | **B = 1**. | | **Isolate DEAR** | $D$ must equal `5` (since *DARE* and *DEAR* start with `5`). | $E$ is 2nd letter in *DEAR*. `5234` has `2` as 2nd digit. | **DEAR = 5234**. | > **Final Match for BEAR:** Starts with $B(1)$, contains $E(2)$, $A(3)$, $R(4)$ $\rightarrow$ **1234**.