12.2 Number-Letter Codes & Substitution Ciphers

Substitution ciphers and number-letter coding problems form a major component of the ISEB Common Pre-Test Verbal Reasoning paper. These questions assess deductive logic, systematic analysis, and precision under time constraints. Instead of testing arbitrary vocabulary recall, cipher problems evaluate how effectively you can isolate structural patterns, build deduction tables on scratch paper, and apply decoded rules to encrypt or decrypt new words.

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Word-to-Code Matching (Scrambled Order)

The most classic and high-yield cipher archetype on the Pre-Test presents a set of four or five words alongside an equal number of multi-digit numeric codes. Crucially, the codes are not listed in the same order as the words.

┌─────────────────────────────────────────────────────────┐
│                     Word-to-Code Set                    │
│ Words: BARK    ROAR    BEAK    LARK                     │
│ Codes: 4125    2312    4915    7125  (Scrambled Order!) │
└─────────────────────────────────────────────────────────┘

Candidates who attempt to guess mappings randomly waste minutes and fall into trap choices. High scorers employ an infallible four-step deduction protocol.

The 4-Step Cracking Protocol

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Step 1: Scan for Structural Fingerprints

Search the words for distinctive structural anomalies:

• Repeated letters within a single word: In the set above, the word ROAR begins and ends with the same letter ($R$). Look at the number codes: only 2312 begins and ends with the same digit ($2$). This single observation cracks the entire cipher immediately!
• Double letters: Words like DEEP (double $E$) or BELL (double $L$) pair instantly with codes containing duplicate adjacent digits (e.g., $9552$ or $3488$).
• Unique terminal letters: If three words end in $K$ and one ends in $R$, the code with the unique ending digit corresponds to the word ending in $R$.

Step 2: Confirm the Anchor Mapping

From the structural match in Step 1:

$$\text{ROAR} = 2312$$

This reveals four immediate letter-digit equivalences:

• $R = 2$
• $O = 3$
• $A = 1$
• $R = 2$ (confirmed)

Step 3: Complete the Cipher Extraction Matrix

Now examine BARK, BEAK and LARK.

• All end in K; the remaining codes 4125, 4915 and 7125 all end in 5, so K = 5.
• BEAK has A in its third position. Since A = 1, its code must have 1 third. Only 4915 does, so B = 4 and E = 9.
• BARK must now start with 4 and follow B–A–R–K, giving 4125. Notice that before identifying B, both 4125 and 7125 fitted the partial pattern ?125; that partial pattern alone was insufficient.
• The remaining word LARK takes 7125, so L = 7.

Step 4: The Master Decoded Key

We now possess a comprehensive, verified mapping for every letter encountered:

With this key, you can encode any new word or decrypt any numeric sequence asked by the question:

• How is BORE encoded? $B(4), O(3), R(2), E(9) \implies \mathbf{4329}$.
• How is LOBE encoded? $L(7), O(3), B(4), E(9) \implies \mathbf{7349}$.
• What word does 7125 represent? $7(L), 1(A), 2(R), 5(K) \implies \mathbf{LARK}$.

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Letter-to-Letter Substitution Ciphers

In letter-to-letter ciphers, one word is transformed into a coded string of letters according to a systematic shift rule:

"If STEAM is coded as TUFBN, how is WATER coded?"

1. Uniform Shift Ciphers (Caesar Ciphers)

Every letter in the word is shifted forward or backward by the same constant amount:

• $S \xrightarrow{+1} T$
• $T \xrightarrow{+1} U$
• $E \xrightarrow{+1} F$
• $A \xrightarrow{+1} B$
• $M \xrightarrow{+1} N$
• The shift is uniformly $+1$.
• Applying this to WATER:
  • $W(23) + 1 = X(24)$
  • $A(1) + 1 = B(2)$
  • $T(20) + 1 = U(21)$
  • $E(5) + 1 = F(6)$
  • $R(18) + 1 = S(19)$
  • Result: $XBUFS$

2. Variable (Progressive) Shift Ciphers

The magnitude of the shift changes depending on the letter's position within the word:

• Position 1: $+1$
• Position 2: $+2$
• Position 3: $+3$
• Position 4: $+4$
• Position 5: $+5$

3. Alternating Shift Ciphers

The operation oscillates between positive and negative shifts across consecutive letters (e.g., $+2, -1, +2, -1$).

4. Mirrored / Reverse Substitution Ciphers

Letters are swapped with their symmetrical counterparts from the opposite end of the alphabet ($A \leftrightarrow Z, B \leftrightarrow Y$). For example, GOLD becomes TLOW because $G(7) + T(20) = 27$, $O(15) + L(12) = 27$, $L(12) + O(15) = 27$, and $D(4) + W(23) = 27$.

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Letter-Number Equations & Arithmetic Logic

Letter-number equations combine substitution rules with elementary algebra and arithmetic order of operations (BIDMAS / BODMAS). Each letter is assigned an integer value, and you must calculate the result of an equation before translating the numeric answer back into its corresponding letter.

Example Problem:

Given the values:

$$A = 3, \quad B = 5, \quad C = 6, \quad D = 14, \quad E = 26$$

Which letter represents the answer to the following expression?

$$(E - D) \div A \times B - C$$

Step-by-step Solution:

1. Substitute the numeric values into the expression: $$(26 - 14) \div 3 \times 5 - 6$$
2. Apply BIDMAS:
   • Brackets first: $(26 - 14) = 12$
   • Division and Multiplication (left-to-right): $$12 \div 3 = 4$$ $$4 \times 5 = 20$$
   • Subtraction: $$20 - 6 = 14$$
3. Map the resulting number back to a letter:
   • Look at the given values: $14$ corresponds to $D$.
   • Answer: $D$

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Common Exam Traps & Avoidance Protocols