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:

$$\begin{aligned} B &\rightarrow X, & O &\rightarrow Q, & A &\rightarrow Z, & T &\rightarrow P \\ T &\rightarrow P, & E &\rightarrow M, & A &\rightarrow Z, & M &\rightarrow R \end{aligned}$$

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.

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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.

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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

Final Match for BEAR: Starts with $B(1)$, contains $E(2)$, $A(3)$, $R(4)$ $\rightarrow$ 1234.