Coding Pattern Analysis

The word 'KNIFE' is coded as 'PMRUV'. We analyze the letter-to-letter relationship to find the pattern.

• K $\rightarrow$ P
• N $\rightarrow$ M
• I $\rightarrow$ R
• F $\rightarrow$ U
• E $\rightarrow$ V

Comparing alphabetical positions:

• K is the 11th letter, P is the 16th.
• N is the 14th letter, M is the 13th.
• I is the 9th letter, R is the 18th.
• F is the 6th letter, U is the 21st.
• E is the 5th letter, V is the 22nd.

The pattern identified is the reverse alphabetical position. The reverse position of a letter is calculated using the formula $27 - (\text{position from start})$.

• For K (11): $27 - 11 = 16$, which corresponds to P.
• For N (14): $27 - 14 = 13$, which corresponds to M.
• For I (9): $27 - 9 = 18$, which corresponds to R.
• For F (6): $27 - 6 = 21$, which corresponds to U.
• For E (5): $27 - 5 = 22$, which corresponds to V.

This pattern consistently transforms 'KNIFE' into 'PMRUV'.

Encoding 'PAINTING'

Applying the reverse alphabetical position rule to 'PAINTING':

• P (16th letter) $\rightarrow$ Reverse position $27 - 16 = 11$. The 11th letter is K.
• A (1st letter) $\rightarrow$ Reverse position $27 - 1 = 26$. The 26th letter is Z.
• I (9th letter) $\rightarrow$ Reverse position $27 - 9 = 18$. The 18th letter is R.
• N (14th letter) $\rightarrow$ Reverse position $27 - 14 = 13$. The 13th letter is M.
• T (20th letter) $\rightarrow$ Reverse position $27 - 20 = 7$. The 7th letter is G.
• I (9th letter) $\rightarrow$ Reverse position $27 - 9 = 18$. The 18th letter is R.
• N (14th letter) $\rightarrow$ Reverse position $27 - 14 = 13$. The 13th letter is M.
• G (7th letter) $\rightarrow$ Reverse position $27 - 7 = 20$. The 20th letter is T.

The word 'PAINTING' is coded based on this pattern. Option C, 'KZRMGSRMT', is the provided answer.