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.
Check Your Progress 3.4
Official CBSE Applied Mathematics Support Material Questions with Step-by-Step Solutions
CYP 3.4.1CBSE Textbook Question
If in the English alphabet, every alternate letter from D onwards is written in capital letters while others are small, how will the 3rd day from Monday be coded?
Counting from Monday as day 1 $\to$ Mon(1), Tue(2), Wed(3) $\implies$ Wednesday. Even letters $\ge 4$ are capitals ($D, F, H, J, L, N, P, R, T, V, X, Z$). Wednesday letters: $w, e, D, N, e, s, D, a, y$ (or matching key: THuRsDay if counted as day offset). Answer: (d) THuRsDay (per textbook answer key) / (b) weDNesDay.
CYP 3.4.2CBSE Textbook Question
If 'white' is called 'yellow', 'yellow' is called 'blue', 'blue' is called 'red', 'red' is called 'black', 'black' is called 'violet', 'violet' is called 'green' and 'green' is called 'orange', what would be the colour if we mix red and green together?
Mixing red and green spectral colors yields yellow. By the substitution rule: 'yellow' is called 'blue'. Answer: (a) Blue.
CYP 3.4.3CBSE Textbook Question
In a code 'MON500N' is written as 'S6T11U6T'. How is 'WINT3R' written?
Each character is shifted by $+6$: • $W(23)+6=29 \equiv 3 \to C$ • $I \to 7$ • $N(14)+6=20 \to T$ • $T(20)+6=26 \to Z$ • $3+6 = 9$ • $R(18)+6=24 \to X$ Answer: (c) C7TZ9X.
Applied Problem-Solving Worksheet
Test your analytical mastery with graded problem sets for Coding-Decoding. Work through each problem systematically.
Speed & Accuracy Drill 1:
Solve all subtopic problems under timed test conditions (15 minutes).