In a certain code language, each letter is replaced by its alphabetical mirror so that the sum of the positions of a letter and its code partner is always 27 (A ↔ Z, B ↔ Y, …, M ↔ N). Under this Atbash style code, UNCOVER is written as FMXLEVI. Using the same code, how is TIP written?

Introduction / Context:
This coding question uses an Atbash style substitution, where each letter is replaced by its mirror in the alphabet. In such a code, the first letter A pairs with Z, B pairs with Y, C with X and so on, so that the sum of the positions of a letter and its coded partner is 27. You are told that UNCOVER is coded as FMXLEVI and must determine how TIP is written under the same system.

Given Data / Assumptions:

• Word: UNCOVER, Code: FMXLEVI.
• The mapping is letter by letter and one to one.
• For Atbash, if a letter is at position n in the alphabet, its code partner is at position 27 - n.
• We need to code TIP using this mapping.

Concept / Approach:
The approach is to verify that UNCOVER → FMXLEVI follows the Atbash rule. If it does, then the same mapping can be applied to any new word, including TIP. To verify, we compute the alphabetical positions of each letter in UNCOVER and FMXLEVI and check that each pair sums to 27. Once confirmed, we use the rule code(letter) = letter at position 27 - original position for T, I and P.

Step-by-Step Solution:
Step 1: Write the letter pairs from UNCOVER to FMXLEVI. U → F, N → M, C → X, O → L, V → E, E → V, R → I. Step 2: Convert each letter to its alphabetical position. U(21) and F(6): 21 + 6 = 27. N(14) and M(13): 14 + 13 = 27. C(3) and X(24): 3 + 24 = 27. O(15) and L(12): 15 + 12 = 27. V(22) and E(5): 22 + 5 = 27. E(5) and V(22): 5 + 22 = 27. R(18) and I(9): 18 + 9 = 27. Step 3: Every pair sums to 27, confirming that this is an Atbash mapping. Step 4: Now code the letters in TIP. T is the 20th letter, so its partner has position 27 - 20 = 7, which is G. I is the 9th letter, so its partner has position 27 - 9 = 18, which is R. P is the 16th letter, so its partner has position 27 - 16 = 11, which is K. Step 5: Combine the coded letters: G R K → GRK.

Verification / Alternative check:
To verify, decode GRK back to TIP by reversing the Atbash mapping. G is 7, so its mirror is 27 - 7 = 20, which is T. R is 18, so its mirror is 27 - 18 = 9, which is I. K is 11, so its mirror is 27 - 11 = 16, which is P. This reconstructs TIP exactly, confirming that GRK is the correct code. Because the mapping works both ways and matches all examples from UNCOVER, it is a robust and consistent rule.

Why Other Options Are Wrong:
Options LTV, NQV, KHQ and LHR involve different letters that do not satisfy the Atbash mirror rule for T, I and P. For example, if T were mapped to L, the positions would be 20 and 12, which sum to 32, not 27. Each wrong option would require abandoning the consistent mirror property established by UNCOVER. Since the code must be the same across all words, only GRK is compatible with the confirmed mapping.

Common Pitfalls:
A common mistake is to look for a fixed forward or backward shift instead of noticing the mirror property. Another is to miscount positions when letters are near the end of the alphabet. Writing down the full alphabet with position numbers and explicitly checking that each letter pair sums to 27 is an effective way to avoid errors. Once the Atbash pattern is recognised, encoding any other word is straightforward.

Final Answer:
Under the Atbash style coding where partnered positions sum to 27, TIP is written as GRK.