10.1: Forward/Backward Shift (Caesar Cipher Type)

 

10.1: Forward/Backward Shift (Caesar Cipher Type)

In these problems, each letter in a word or sequence is shifted forward or backward in the alphabet by a fixed number of positions. For example, a forward shift of 2 turns A into C, B into D, etc.

Problems and Solutions

Problem 1: If each letter in the word "CAT" is shifted forward by 2 positions, what is the new word?
Solution:

• Step 1: Identify the letters: C, A, T.
• Step 2: Determine their positions: C=3, A=1, T=20.
• Step 3: Apply the forward shift of 2:
  • C: 3 + 2 = 5 → E
  • A: 1 + 2 = 3 → C
  • T: 20 + 2 = 22 → V
• Step 4: Combine the new letters: E, C, V → ECV.
  Explanation: Each letter’s position in the alphabet is increased by 2, and the corresponding new letters form the word "ECV".

Problem 2: Shift each letter in "DOG" backward by 3 positions.
Solution:

• Step 1: Letters: D, O, G.
• Step 2: Positions: D=4, O=15, G=7.
• Step 3: Apply backward shift of 3:
  • D: 4 - 3 = 1 → A
  • O: 15 - 3 = 12 → L
  • G: 7 - 3 = 4 → D
• Step 4: New word: ALD.
  Explanation: Subtracting 3 from each letter’s position gives the new letters A, L, D.

Problem 3: What is the result of shifting "ZEBRA" forward by 1?
Solution:

• Step 1: Letters: Z, E, B, R, A.
• Step 2: Positions: Z=26, E=5, B=2, R=18, A=1.
• Step 3: Shift forward by 1:
  • Z: 26 + 1 = 27 → 27-26 = 1 → A (wrap around).
  • E: 5 + 1 = 6 → F
  • B: 2 + 1 = 3 → C
  • R: 18 + 1 = 19 → S
  • A: 1 + 1 = 2 → B
• Step 4: New word: AFCSB.
  Explanation: For Z, the shift exceeds 26, so we subtract 26 to wrap around to A.

Problem 4: Shift "KEY" backward by 2.
Solution:

• Letters: K=11, E=5, Y=25.
• Backward shift by 2:
  • K: 11 - 2 = 9 → I
  • E: 5 - 2 = 3 → C
  • Y: 25 - 2 = 23 → W
• New word: ICW.
  Explanation: Each letter moves back two positions in the alphabet.

Problem 5: Shift "BALL" forward by 4.
Solution:

• Letters: B=2, A=1, L=12, L=12.
• Forward shift by 4:
  • B: 2 + 4 = 6 → F
  • A: 1 + 4 = 5 → E
  • L: 12 + 4 = 16 → P
  • L: 12 + 4 = 16 → P
• New word: FEPP.
  Explanation: Add 4 to each letter’s position to get the new letters.

Problem 6: Shift "WXYZ" backward by 5.
Solution:

• Letters: W=23, X=24, Y=25, Z=26.
• Backward shift by 5:
  • W: 23 - 5 = 18 → R
  • X: 24 - 5 = 19 → S
  • Y: 25 - 5 = 20 → T
  • Z: 26 - 5 = 21 → U
• New word: RSTU.
  Explanation: Subtract 5 from each position to find the new letters.

Problem 7: Shift "HIJ" forward by 3.
Solution:

• Letters: H=8, I=9, J=10.
• Forward shift by 3:
  • H: 8 + 3 = 11 → K
  • I: 9 + 3 = 12 → L
  • J: 10 + 3 = 13 → M
• New word: KLM.
  Explanation: Each letter advances three positions.

Problem 8: Shift "SUN" backward by 1.
Solution:

• Letters: S=19, U=21, N=14.
• Backward shift by 1:
  • S: 19 - 1 = 18 → R
  • U: 21 - 1 = 20 → T
  • N: 14 - 1 = 13 → M
• New word: RTM.
  Explanation: Move each letter back one position.

Problem 9: Shift "APPLE" forward by 5.
Solution:

• Letters: A=1, P=16, P=16, L=12, E=5.
• Forward shift by 5:
  • A: 1 + 5 = 6 → F
  • P: 16 + 5 = 21 → U
  • P: 16 + 5 = 21 → U
  • L: 12 + 5 = 17 → Q
  • E: 5 + 5 = 10 → J
• New word: FUUQJ.
  Explanation: Add 5 to each position to get the new word.

Problem 10: Shift "QUIZ" backward by 4.
Solution:

• Letters: Q=17, U=21, I=9, Z=26.
• Backward shift by 4:
  • Q: 17 - 4 = 13 → M
  • U: 21 - 4 = 17 → Q
  • I: 9 - 4 = 5 → E
  • Z: 26 - 4 = 22 → V
• New word: MQEV.
  Explanation: Subtract 4 from each position to get the new letters.