Decoding the Alphabet Pattern

The problem presents a coding challenge where words are transformed based on a specific rule. We need to find this rule by analyzing the given examples: 'NATION' becomes 'MZGRLM' and 'PRINTS' becomes 'KIRMGH'.

Identifying the Coding Logic

Let's examine the relationship between the letters in the original words and their coded counterparts. Consider the alphabet positions (A=1, B=2, ..., Z=26).

For 'NATION' to 'MZGRLM':

• N (14) -> M (13)
• A (1) -> Z (26)
• T (20) -> G (7)
• I (9) -> R (18)
• O (15) -> L (12)
• N (14) -> M (13)

Notice that each coded letter is the reverse alphabet counterpart of the original letter. For instance, N is the 14th letter, and its reverse is the (27-14)=13th letter, which is M. Similarly, A (1st) reverses to Z (26th), T (20th) reverses to G (7th), and so on.

Let's verify this pattern with 'PRINTS' to 'KIRMGH':

• P (16) -> K (11), since 27-16 = 11
• R (18) -> I (9), since 27-18 = 9
• I (9) -> R (18), since 27-9 = 18
• N (14) -> M (13), since 27-14 = 13
• T (20) -> G (7), since 27-20 = 7
• S (19) -> H (8), since 27-19 = 8

The reverse alphabet substitution rule holds true for both examples.

Applying the Code to 'BOTTLE'

Now, we apply the same reverse alphabet substitution rule to the word 'BOTTLE':

• B is the 2nd letter. Its reverse is the (27-2) = 25th letter, which is Y.
• O is the 15th letter. Its reverse is the (27-15) = 12th letter, which is L.
• T is the 20th letter. Its reverse is the (27-20) = 7th letter, which is G.
• T is the 20th letter. Its reverse is the (27-20) = 7th letter, which is G.
• L is the 12th letter. Its reverse is the (27-12) = 15th letter, which is O.
• E is the 5th letter. Its reverse is the (27-5) = 22nd letter, which is V.

Combining these results, 'BOTTLE' is coded as 'YLGGOV'.