10.3: Pattern-Based Substitution

 

10.3: Pattern-Based Substitution

Letters are replaced based on a pattern, such as alternating shifts, positional rules, or arithmetic operations.

Problems and Solutions

Problem 1: In "BOOK", shift odd-positioned letters forward by 2, even-positioned backward by 1.
Solution:

• Step 1: Letters: B=2, O=15, O=15, K=11. Positions: 1, 2, 3, 4.
• Step 2: Apply pattern:
  • Pos 1 (odd): B: 2 + 2 = 4 → D
  • Pos 2 (even): O: 15 - 1 = 14 → N
  • Pos 3 (odd): O: 15 + 2 = 17 → Q
  • Pos 4 (even): K: 11 - 1 = 10 → J
• Step 3: New word: DNQJ.
  Explanation: Odd positions shift forward by 2, even positions backward by 1.

Problem 2: In "STAR", shift each letter by its position number forward.
Solution:

• Step 1: Letters: S=19, T=20, A=1, R=18.
• Step 2: Shift by position:
  • Pos 1: S: 19 + 1 = 20 → T
  • Pos 2: T: 20 + 2 = 22 → V
  • Pos 3: A: 1 + 3 = 4 → D
  • Pos 4: R: 18 + 4 = 22 → V
• Step 3: New word: TVDV.
  Explanation: Each letter’s position is increased by its position number.

Problem 3: In "CUTE", shift even-positioned letters backward by 3, odd forward by 2.
Solution:

• Letters: C=3, U=21, T=20, E=5.
• Apply pattern:
  • Pos 1 (odd): C: 3 + 2 = 5 → E
  • Pos 2 (even): U: 21 - 3 = 18 → R
  • Pos 3 (odd): T: 20 + 2 = 22 → V
  • Pos 4 (even): E: 5 - 3 = 2 → B
• New word: ERVB.
  Explanation: Alternate shifts based on position.

Problem 4: In "MATH", shift each letter by twice its position backward.
Solution:

• Letters: M=13, A=1, T=20, H=8.
• Shift by 2×position backward:
  • Pos 1: M: 13 - 2×1 = 11 → K
  • Pos 2: A: 1 - 2×2 = 1 - 4 = 23 → W (1-4=-3, add 26).
  • Pos 3: T: 20 - 2×3 = 14 → N
  • Pos 4: H: 8 - 2×4 = 0 → 26 → Z
• New word: KWNZ.
  Explanation: Each letter shifts back by twice its position.

Problem 5: In "FIVE", shift odd positions forward by 1, even by 2.
Solution:

• Letters: F=6, I=9, V=22, E=5.
• Apply pattern:
  • Pos 1 (odd): F: 6 + 1 = 7 → G
  • Pos 2 (even): I: 9 + 2 = 11 → K
  • Pos 3 (odd): V: 22 + 1 = 23 → W
  • Pos 4 (even): E: 5 + 2 = 7 → G
• New word: GKWG.
  Explanation: Different shifts for odd and even positions.

Problem 6: In "KING", shift each letter by position number forward, but reverse the word.
Solution:

• Letters: K=11, I=9, N=14, G=7.
• Shift by position forward:
  • Pos 1: K: 11 + 1 = 12 → L
  • Pos 2: I: 9 + 2 = 11 → K
  • Pos 3: N: 14 + 3 = 17 → Q
  • Pos 4: G: 7 + 4 = 11 → K
• Reverse: LKQK → KQLK.
  Explanation: Shift by position, then reverse the resulting word.

Problem 7: In "WOLF", shift each letter by (position + 1) backward.
Solution:

• Letters: W=23, O=15, L=12, F=6.
• Shift by (pos + 1) backward:
  • Pos 1: W: 23 - (1+1) = 21 → U
  • Pos 2: O: 15 - (2+1) = 12 → L
  • Pos 3: L: 12 - (3+1) = 8 → I
  • Pos 4: F: 6 - (4+1) = 1 → A
• New word: ULIA.
  Explanation: Shift each letter back by position + 1.

Problem 8: In "BELL", shift odd positions forward by 3, even backward by 2.
Solution:

• Letters: B=2, E=5, L=12, L=12.
• Apply pattern:
  • Pos 1 (odd): B: 2 + 3 = 5 → E
  • Pos 2 (even): E: 5 - 2 = 3 → C
  • Pos 3 (odd): L: 12 + 3 = 15 → O
  • Pos 4 (even): L: 12 - 2 = 10 → J
• New word: ECOJ.
  Explanation: Alternate shifts based on position.

Problem 9: In "MOON", shift each letter by position squared forward.
Solution:

• Letters: M=13, O=15, O=15, N=14.
• Shift by pos² forward:
  • Pos 1: M: 13 + 1² = 14 → N
  • Pos 2: O: 15 + 2² = 19 → S
  • Pos 3: O: 15 + 3² = 24 → X
  • Pos 4: N: 14 + 4² = 30 → 30-26 = 4 → D
• New word: NSXD.
  Explanation: Shift by the square of the position.

Problem 10: In "RACE", shift even positions forward by 4, odd backward by 2.
Solution:

• Letters: R=18, A=1, C=3, E=5.
• Apply pattern:
  • Pos 1 (odd): R: 18 - 2 = 16 → P
  • Pos 2 (even): A: 1 + 4 = 5 → E
  • Pos 3 (odd): C: 3 - 2 = 1 → A
  • Pos 4 (even): E: 5 + 4 = 9 → I
• New word: PEAI.
  Explanation: Different shifts for odd and even positions.