3.4 Determining the Shift Pattern or Original Sequence

 3.4  Determining the Shift Pattern or Original Sequence - Practice

Description: The resulting sequence or word after alternating shifts is given, and the task is to determine the original sequence, the shift amounts, or the alternating pattern used. This is a reverse-engineering problem, often requiring deduction.

Example Question: The sequence D, E, I, I is obtained by applying alternating shifts to an original sequence of 4 letters. Odd-positioned letters were shifted forward by 2, and even-positioned letters were shifted forward by 3. What was the original sequence?

• Solution:
  • For odd positions (1st, 3rd), reverse the +2 shift: -2.
  • For even positions (2nd, 4th), reverse the +3 shift: -3.
  • D (1st, odd): D (4) - 2 = 2 → B.
  • E (2nd, even): E (5) - 3 = 2 → B.
  • I (3rd, odd): I (9) - 2 = 7 → G.
  • I (4th, even): I (9) - 3 = 6 → F.
  • Original sequence: B, B, G, F.

Key Focus: Working backward to deduce the original sequence or shift pattern based on the given result and rules.

Variants:

• Find the original sequence given the shifted sequence and shift rules.
• Determine the shift amounts or directions (e.g., what shifts produce the given result?).
• Identify the alternating pattern (e.g., is it odd/even-based or a repeating cycle?).
• Verify if a given sequence could result from specific alternating shifts.