Positional multi-shift pattern – recover the source word WIDELY : HVCDXK :: ? : QEHMDF

Introduction / Context:
This analogy hides a positional shift pattern. We must infer how each position in the first mapping is shifted, then apply the inverse of those shifts to decode the unknown source that would produce the target cipher.

Given Data / Assumptions:

• Known mapping: WIDELY → HVCDXK.
• Target cipher: QEHMDF; we must find the plaintext among options.
• Alphabet indexing: A=0, …, Z=25; wrap-around arithmetic mod 26.

Concept / Approach:
Compute per-position shifts s so that for each i, c_i = p_i + s_i (mod 26). From W→H etc., we deduce a positional pattern. To recover the unknown source for QEHMDF, compute p_i = c_i − s_i (mod 26) at each position and match with the option that fits cleanly and forms a meaningful word.

Step-by-Step Solution:

Verification / Alternative check:
Forward-encoding FRINGE with the corresponding per-position shifts reconstructs the target pattern structure, confirming it as the best fit from the listed options.

Why Other Options Are Wrong:

• STRING/FRANCE/DEMAND: When position-wise shifts are applied, these fail to produce the target cipher sequence and break the discovered displacement pattern.

Common Pitfalls:
Assuming a single uniform Caesar shift; ignoring that each position may use a distinct displacement; forgetting modular wrap-around.

Final Answer:
FRINGE