In a certain code language, the English word "QUICKLY" is written as "OSGAIJW". Using the same systematic shift of letters, how will the word "HUE" be written in that code language?

Introduction:
This coding and decoding question uses a consistent shift of letters in the alphabet. The word QUICKLY is coded as OSGAIJW. Our task is to determine the rule that maps each original letter to its coded partner, and then apply that rule to the letters of HUE. This tests comfort with basic Caesar shift style ciphers in the alphabet.

Given Data / Assumptions:
The mapping is QUICKLY → OSGAIJW. We assume:
1) Each letter is replaced by exactly one other letter.
2) A fixed shift (forward or backward) is applied to all letters.
3) The alphabet wraps around cyclically from A to Z and from Z to A if needed.

Concept / Approach:
To find the shift, we compare the positions of corresponding letters from QUICKLY and OSGAIJW. If the difference in positions is constant across every pair, we have identified a Caesar shift. Once we know whether the shift is forward or backward and by how many positions, we can apply it to H, U, and E in the word HUE.

Step-by-Step Solution:
Step 1: List positions for QUICKLY: Q=17, U=21, I=9, C=3, K=11, L=12, Y=25.Step 2: List positions for OSGAIJW: O=15, S=19, G=7, A=1, I=9, J=10, W=23.Step 3: Find the shift: Q to O is 17 to 15 (minus 2), U to S is 21 to 19 (minus 2), I to G is 9 to 7 (minus 2), C to A is 3 to 1 (minus 2), K to I is 11 to 9 (minus 2), L to J is 12 to 10 (minus 2), and Y to W is 25 to 23 (minus 2).Step 4: Since each letter is shifted back by 2 positions, the code rule is: coded letter = original letter shifted backward by 2.Step 5: Apply this shift to HUE. H is 8 and becomes F (6), U is 21 and becomes S (19), E is 5 and becomes C (3).Step 6: Therefore, HUE is written as FSC in the code language.

Verification / Alternative check:
If we shift each letter of FSC forward by 2 positions, we should obtain HUE. F becomes H, S becomes U, and C becomes E. This confirms that the shift has been applied correctly, and the cipher is internally consistent for this word as well as for QUICKLY.

Why Other Options Are Wrong:
The options ZMA, HZK, HNI, and GTC do not result from a uniform backward shift of 2 applied to H, U, and E. Each of these options would require different shifts for different letters or a forward shift, which contradicts the pattern derived from QUICKLY → OSGAIJW.

Common Pitfalls:
One common mistake is miscounting when shifting backward, especially near the start of the alphabet. Another is to identify the wrong shift magnitude because only the first pair of letters was checked. Always validate the hypothesised shift by testing it against every letter pair in the given example word.

Final Answer:
The word "HUE" is written as FSC in the given code language.