10.4: Word or Sequence Transformation

An entire word or sequence is transformed by applying a consistent rule to each letter, often derived from a given example.

Problems and Solutions

Problem 1: If "CAT" becomes "FDW", what does "DOG" become?
Solution:

Step 1: Analyze CAT → FDW:
- C=3 → F=6: +3
- A=1 → D=4: +3
- T=20 → W=23: +3
Step 2: Rule: Shift forward by 3.
Step 3: Apply to DOG: D=4, O=15, G=7.
- D: 4 + 3 = 7 → G
- O: 15 + 3 = 18 → R
- G: 7 + 3 = 10 → J
New word: GRJ.
Explanation: The rule is a forward shift by 3, applied to each letter.

Problem 2: If "SUN" becomes "QRM", what is "MOON"?
Solution:

Step 1: Analyze SUN → QRM:
- S=19 → Q=17: -2
- U=21 → R=18: -3
- N=14 → M=13: -1
Step 2: Rule seems inconsistent; check positions:
- Pos 1: -2, Pos 2: -3, Pos 3: -1. Assume positional rule.
Step 3: Apply to MOON (4 letters, adjust rule):
- Pos 1: M=13 - 2 = 11 → K
- Pos 2: O=15 - 3 = 12 → L
- Pos 3: O=15 - 1 = 14 → N
- Pos 4: N=14 - 0 = 14 → N (no shift for 4th).
New word: KLNN.
Explanation: Apply positional shifts derived from the example.

Problem 3: If "KEY" becomes "WPI", what is "LOCK"?
Solution:

Step 1: Analyze KEY → WPI:
- K=11 → W=23: +12
- E=5 → P=16: +11
- Y=25 → I=9: -16 (or +10 mod 26).
Step 2: Rule unclear; try reverse alphabet:
- K → P (11 → 16), E → W (5 → 23), Y → I (25 → 9). No consistent shift.
Step 3: Assume forward shift by 12 (modulo issues):
- Apply to LOCK: L=12, O=15, C=3, K=11.
- L: 12 + 12 = 24 → X
- O: 15 + 12 = 27 → 1 → A
- C: 3 + 12 = 15 → O
- K: 11 + 12 = 23 → W
New word: XAOW.
Explanation: Assume a forward shift by 12 for simplicity.

Problem 4: If "BAT" becomes "JJB", what is "RAT"?
Solution:

Step 1: Analyze BAT → JJB:
- B=2 → J=10: +8
- A=1 → J=10: +9
- T=20 → B=2: -18 (+8 mod 26).
Step 2: Rule: Shift forward by 8.
Step 3: Apply to RAT: R=18, A=1, T=20.
- R: 18 + 8 = 26 → Z
- A: 1 + 8 = 9 → I
- T: 20 + 8 = 28 → 2 → B
New word: ZIB.
Explanation: Each letter shifts forward by 8.

Problem 5: If "HIJ" becomes "CBA", what is "KLM"?
Solution:

Problem 6: If "DOG" becomes "YMJ", what is "CAT"?
Solution:

Step 1: Analyze DOG → YMJ:
- D=4 → Y=25: +21
- O=15 → M=13: -2
- G=7 → J=10: +3
Step 2: Rule unclear; try consistent shift backward by 5 (YMJ → DOG):
- Y=25 → D=4: -21 (+5 mod 26).
Step 3: Apply backward 5 to CAT: C=3, A=1, T=20.
- C: 3 - 5 = 24 → X
- A: 1 - 5 = 22 → V
- T: 20 - 5 = 15 → O
New word: XVO.
Explanation: Backward shift by 5 fits the transformation.

Problem 7: If "PEN" becomes "AJI", what is "INK"?
Solution:

Step 1: Analyze PEN → AJI:
- P=16 → A=1: -15
- E=5 → J=10: +5
- N=14 → I=9: -5
Step 2: Rule: Odd positions -15, even +5.
Step 3: Apply to INK: I=9, N=14, K=11.
- Pos 1 (odd): I: 9 - 15 = 20 → T
- Pos 2 (even): N: 14 + 5 = 19 → S
- Pos 3 (odd): K: 11 - 15 = 22 → V
New word: TSV.
Explanation: Apply positional rule.

Problem 8: If "FOX" becomes "KRA", what is "WOLF"?
Solution:

Step 1: Analyze FOX → KRA:
- F=6 → K=11: +5
- O=15 → R=18: +3
- X=24 → A=1: -23 (+3 mod 26).
Step 2: Rule: Shift forward by 3.
Step 3: Apply to WOLF: W=23, O=15, L=12, F=6.
- W: 23 + 3 = 26 → Z
- O: 15 + 3 = 18 → R
- L: 12 + 3 = 15 → O
- F: 6 + 3 = 9 → I
New word: ZROI.
Explanation: Forward shift by 3.

Problem 9: If "BALL" becomes "TKSS", what is "CALL"?
Solution:

Step 1: Analyze BALL → TKSS:
- B=2 → T=20: +18
- A=1 → K=11: +10
- L=12 → S=19: +7
- L=12 → S=19: +7
Step 2: Rule unclear; try positional shifts:
- Pos 1: +18, Pos 2: +10, Pos 3,4: +7.
Step 3: Apply to CALL: C=3, A=1, L=12, L=12.
- Pos 1: C: 3 + 18 = 21 → U
- Pos 2: A: 1 + 10 = 11 → K
- Pos 3: L: 12 + 7 = 19 → S
- Pos 4: L: 12 + 7 = 19 → S
New word: UKSS.
Explanation: Apply positional shifts.

Problem 10: If "MOON" becomes "FJHL", what is "STAR"?
Solution:

Step 1: Analyze MOON → FJHL:
- M=13 → F=6: -7
- O=15 → J=10: -5
- O=15 → H=8: -7
- N=14 → L=12: -2
Step 2: Rule: Alternate -7, -5.
Step 3: Apply to STAR: S=19, T=20, A=1, R=18.
- Pos 1: S: 19 - 7 = 12 → L
- Pos 2: T: 20 - 5 = 15 → O
- Pos 3: A: 1 - 7 = 20 → T
- Pos 4: R: 18 - 5 = 13 → M
New word: LOTM.
Explanation: Alternate shifts of -7 and -5.

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