Chapter 3 • Unit II • Section 3.4

Exercise 3.4: Coding-Decoding

Decipher substitution ciphers, positional letter shifts, reverse ciphers, case alternation, and numerical positional average sums.

Core Theoretical Principles

Systematic principles and analytical strategies prescribed by the CBSE curriculum for Coding-Decoding.

Alphabetical Positional Values & Shifts:
• Forward positions: $A=1, B=2, \dots, Z=26$.
• Memory anchor: $E(5), J(10), O(15), T(20), Y(25)$ (EJOTY).
• Shift cipher: $C_i = (P_i + k) \pmod{26}$.
Reverse & Symmetry Ciphers:
• Opposite letters: $P_i + C_i = 27$ (e.g. $A-Z, B-Y, C-X, D-W, E-V$).
• Reversal cipher: Predecessor or successor written in inverted string order.
Word & Alphanumeric Matrix Decoding:
• Common word elimination: Compare multiple coded phrases to isolate code words.
• Arithmetic mapping: Word value $= \frac{\sum \text{positions}}{2}$ or $(\sum \text{positions}) \times k$.

Solved Illustrative Examples

Example 1 (Reverse Predecessor Cipher)
In a certain code 'LION' is written as 'MNHK'. How is 'MONKEY' written in that code?
Step 1: Analyze LION $\to$ MNHK:
• Predecessor letters: $L-1=K, I-1=H, O-1=N, N-1=M$
• Reversing $K, H, N, M$ gives $M, N, H, K$.
Step 2: Apply to MONKEY:
• Predecessors: $M-1=L, O-1=N, N-1=M, K-1=J, E-1=D, Y-1=X$
• Reversing $L, N, M, J, D, X$ gives $\mathbf{XDJMNL}$.
Answer: (b) XDJMNL.
Example 2 (Word Elimination)
In a code, '564' means 'all the best', '736' means 'best of luck', '423' means 'all is luck'. What is the code for 'all'?
Step 1: Compare '564' (all the best) and '423' (all is luck). The common word is all and the common digit is 4.
Answer: (b) 4.
Example 3 (Positional Sum Average)
In a code 'ENTHALPY' is written as '50.5'. How is 'ENTROPY' written?
Step 1: Sum positions of ENTHALPY: $5+14+20+8+1+12+16+25 = 101$.
Step 2: $\text{Code} = 101 / 2 = 50.5$.
Step 3: Sum positions of ENTROPY: $5+14+20+18+15+16+25 = 113$.
Step 4: $\text{Code} = 113 / 2 = \mathbf{56.5}$.
Answer: (c) 56.5.
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