Difficulty: Medium
Correct Answer: HZK
Explanation:
Introduction / Context:
This question uses a specific substitution cipher where each letter is replaced by its \"mirror\" letter in the alphabet. The word FOREIGN is coded as ULIVRTM. We must use the same rule to code the word SAP.
Given Data / Assumptions:
Concept / Approach:
By examining letter pairs such as F → U, O → L, and R → I, we notice that the positions of the original letter and the coded letter add up to 27. This is the Atbash pattern: each letter is replaced by the letter symmetrically opposite to it in the alphabet (A ↔ Z, B ↔ Y, C ↔ X, and so on).
Step-by-Step Solution:
Step 1: Verify the Atbash pattern on FOREIGN.
F is 6, U is 21; 6 + 21 = 27.
O is 15, L is 12; 15 + 12 = 27.
R is 18, I is 9; 18 + 9 = 27.
E is 5, V is 22; 5 + 22 = 27.
G is 7, T is 20; 7 + 20 = 27.
N is 14, M is 13; 14 + 13 = 27.
Step 2: The rule is confirmed: cipher letter position = 27 − original letter position.
Step 3: Apply this rule to SAP.
S is 19; 27 − 19 = 8 → H.
A is 1; 27 − 1 = 26 → Z.
P is 16; 27 − 16 = 11 → K.
Step 4: Therefore, SAP is coded as HZK.
Verification / Alternative check:
We can recheck by applying the same mirror rule to another letter from FOREIGN, such as I. The mirror of I (9) is R (18) because 9 + 18 = 27, which matches the given code. This confirms that the Atbash mapping is correct.
Why Other Options Are Wrong:
Options NOL, PLQ, and GYP do not follow the 27-sum rule for all three letters of SAP. Their letters correspond to the wrong mirror positions and therefore violate the established Atbash pattern.
Common Pitfalls:
Students sometimes assume a fixed forward or backward shift (like +2) instead of checking the symmetric mirror property. Another mistake is miscounting alphabet ranks or mixing up numerical positions of letters.
Final Answer:
Using the same Atbash mirror coding, SAP is written as HZK in that code language.
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