In a certain code language, the English word "FLOTSAM" is written as "UOLGHZN". Using the same letter substitution pattern, how will the word "PIN" be written in that code language?

Introduction:
This coding and decoding problem is based on a positional substitution cipher applied to letters of the alphabet. The word FLOTSAM is written as UOLGHZN in a certain code. We must uncover the exact transformation and apply it to the word PIN. This tests familiarity with simple alphabet-based ciphers and careful matching of individual letters.

Given Data / Assumptions:
The code language maps FLOTSAM to UOLGHZN. We assume:
1) Each letter of the original word is replaced by exactly one letter in the code word.
2) The transformation is consistent for every occurrence of a given letter.
3) The same substitution pattern is used for any other word, including PIN.

Concept / Approach:
One of the classic coding patterns in such questions is the mirror or Atbash cipher, where A pairs with Z, B with Y, C with X, and so on. To test if this is the case, we compare each letter of FLOTSAM with the corresponding letter in UOLGHZN and see whether each is its mirror in the alphabet. If this holds for every letter, we confidently apply the same mapping to P, I, and N.

Step-by-Step Solution:
Step 1: Pair the letters: F with U, L with O, O with L, T with G, S with H, A with Z, and M with N.Step 2: In an Atbash style mapping, A maps to Z, B to Y, C to X, D to W, E to V, F to U, and so on. Check each pair: F indeed mirrors to U, L to O, O to L, T to G, S to H, A to Z, and M to N.Step 3: Since every pair fits the mirror pattern, the code uses the alphabet reversal rule.Step 4: Apply the same rule to P, I, and N. The mirror of P is K, because P is the sixteenth letter and K is the eleventh (positions summing to 27). The mirror of I is R, and the mirror of N is M.Step 5: Therefore, PIN is encoded as KRM in this code language.

Verification / Alternative check:
If we reverse the mapping for the code KRM, we should come back to PIN. Using the same Atbash rule, K maps back to P, R maps back to I, and M maps back to N. This two way consistency confirms that our understanding of the cipher is correct.

Why Other Options Are Wrong:
GEH, OBI, DVW, and RKO cannot all be produced by the alphabet reversal cipher starting from P, I, and N. Each of those options places at least one letter that is not the correct mirror partner of the original letter, so they violate the discovered pattern.

Common Pitfalls:
Students sometimes attempt to view the code as a simple fixed shift (for example, plus two or minus three) without checking the full set of letter pairs. Others stop after confirming the pattern for only one or two letters instead of checking all of them. A reliable solution always verifies that the inferred rule fits every letter in the given example.

Final Answer:
The word "PIN" is written as KRM in the given code language.