10.2: Letter-to-Letter Mapping (Direct Substitution)

 

2: Letter-to-Letter Mapping (Direct Substitution)

In these problems, each letter is replaced by another specific letter based on a given mapping or code (e.g., A → D, B → E).

Problems and Solutions

Problem 1: If A → C, B → D, C → E, ..., what is the code for "BAD"?
Solution:

• Step 1: The mapping is a forward shift by 2 (A=1 → C=3, B=2 → D=4, etc.).
• Step 2: Letters: B=2, A=1, D=4.
• Step 3: Apply mapping:
  • B → D
  • A → C
  • D → F
• Step 4: New word: DCF.
  Explanation: Each letter is replaced by the letter two positions ahead.

Problem 2: If A → Z, B → Y, C → X, ..., what is the code for "CAT"?
Solution:

• Step 1: Mapping is reverse alphabet: A Z, B Y, etc.
• Step 2: Letters: C=3, A=1, T=20.
• Step 3: Apply mapping:
  • C → X (3rd from start → 3rd from end).
  • A → Z
  • T → I (20th from start → 20th from end).
• Step 4: New word: XZI.
  Explanation: Each letter is replaced by its reverse alphabet counterpart.

Problem 3: If A → K, B → L, C → M, ..., what is "DOG"?
Solution:

• Step 1: Mapping is forward shift by 10 (A=1 → K=11, B=2 → L=12).
• Step 2: Letters: D=4, O=15, G=7.
• Step 3: Apply mapping:
  • D → N (4 + 10 = 14).
  • O → Y (15 + 10 = 25).
  • G → Q (7 + 10 = 17).
• Step 4: New word: NYQ.
  Explanation: Add 10 to each letter’s position.

Problem 4: If A → B, B → C, ..., Z → A, what is "KEY"?
Solution:

• Step 1: Mapping is forward shift by 1.
• Step 2: Letters: K=11, E=5, Y=25.
• Step 3: Apply mapping:
  • K → L
  • E → F
  • Y → Z
• Step 4: New word: LFZ.
  Explanation: Each letter shifts forward by 1.

Problem 5: If A → Y, B → X, C → W, ..., what is "SUN"?
Solution:

• Step 1: Mapping is A → Y (1 → 25), B → X (2 → 24), so position n → 27-n.
• Step 2: Letters: S=19, U=21, N=14.
• Step 3: Apply mapping:
  • S: 27-19 = 8 → I
  • U: 27-21 = 6 → F
  • N: 27-14 = 13 → M
• Step 4: New word: IFM.
  Explanation: Each letter’s position is transformed using 27-n.

Problem 6: If A → E, B → I, C → O, ..., what is "BAT"?
Solution:

• Step 1: Mapping: A=1 → E=5, B=2 → I=9, C=3 → O=15. Pattern is n → n² + 4 (1→5, 2→8, 3→13).
• Step 2: Letters: B=2, A=1, T=20.
• Step 3: Apply mapping:
  • B: 2² + 4 = 8 → I
  • A: 1² + 4 = 5 → E
  • T: 20² + 4 = 404 → 404 mod 26 = 12 → L
• Step 4: New word: IEL.
  Explanation: Each letter’s position is transformed by n² + 4, modulo 26.

Problem 7: If A → M, B → N, ..., what is "HIJ"?
Solution:

• Step 1: Mapping is forward shift by 12 (A=1 → M=13).
• Step 2: Letters: H=8, I=9, J=10.
• Step 3: Apply mapping:
  • H: 8 + 12 = 20 → T
  • I: 9 + 12 = 21 → U
  • J: 10 + 12 = 22 → V
• Step 4: New word: TUV.
  Explanation: Add 12 to each position.

Problem 8: If A → J, B → K, ..., what is "PEN"?
Solution:

• Step 1: Mapping is forward shift by 9 (A=1 → J=10).
• Step 2: Letters: P=16, E=5, N=14.
• Step 3: Apply mapping:
  • P: 16 + 9 = 25 → Y
  • E: 5 + 9 = 14 → N
  • N: 14 + 9 = 23 → W
• Step 4: New word: YNW.
  Explanation: Add 9 to each position.

Problem 9: If A → X, B → W, C → U, ..., what is "CAR"?
Solution:

• Step 1: Mapping: A=1 → X=24, B=2 → W=23. Pattern is n → 25-n.
• Step 2: Letters: C=3, A=1, R=18.
• Step 3: Apply mapping:
  • C: 25-3 = 22 → V
  • A: 25-1 = 24 → X
  • R: 25-18 = 7 → G
• Step 4: New word: VXG.
  Explanation: Each position is transformed using 25-n.

Problem 10: If A → G, B → I, C → K, ..., what is "FOX"?
Solution:

• Step 1: Mapping: A=1 → G=7, B=2 → I=9, C=3 → K=11. Pattern is n → 2n + 5.
• Step 2: Letters: F=6, O=15, X=24.
• Step 3: Apply mapping:
  • F: 2×6 + 5 = 17 → Q
  • O: 2×15 + 5 = 35 → 35-26 = 9 → I
  • X: 2×24 + 5 = 53 → 53-26 = 27 → 1 → A
• Step 4: New word: QIA.
  Explanation: Each position is transformed by 2n + 5, modulo 26.