Understanding the Letter Coding Puzzle

The question asks us to identify which pair among the given options does not follow the same letter-coding pattern as the others. We need to find the underlying rule connecting four pairs and then spot the exception.

Analyzing the Coding Pattern: Complementary Letters

A common coding technique in these types of puzzles involves using 'complementary letters'. In the standard English alphabet (A-Z), letters can be paired such that their positions sum to 27. For example, A (position 1) is complementary to Z (position 26), because \(1 + 26 = 27\). Similarly, B (position 2) pairs with Y (position 25) (\(2 + 25 = 27\)), and C (position 3) pairs with X (position 24) (\(3 + 24 = 27\)).

We will examine each given pair to determine if the letters in the coded word are complementary to the letters in the original word. We'll use 'C' to denote a complementary mapping and 'N' to denote a non-complementary mapping.

Step-by-Step Analysis of Each Pair

We assign numerical positions to letters (\(A=1, B=2, ..., Z=26\)). A pair of letters is considered complementary if the sum of their positions equals 27.

1. CRUSH : XIFSH

• C (position 3) maps to X (position 24). Calculation: \(3 + 24 = 27\). This is a Complementary mapping (C).
• R (position 18) maps to I (position 9). Calculation: \(18 + 9 = 27\). This is a Complementary mapping (C).
• U (position 21) maps to F (position 6). Calculation: \(21 + 6 = 27\). This is a Complementary mapping (C).
• S (position 19) maps to S (position 19). Calculation: \(19 + 19 = 38\). Since \(38 \neq 27\), this is a Non-complementary mapping (N). (The complement of S is H).
• H (position 8) maps to H (position 8). Calculation: \(8 + 8 = 16\). Since \(16 \neq 27\), this is a Non-complementary mapping (N). (The complement of H is S).

The coding pattern for CRUSH is: C, C, C, N, N. There are 2 Non-complementary mappings.

2. FROWN : UILRM

• F (position 6) maps to U (position 21). Calculation: \(6 + 21 = 27\). Complementary (C).
• R (position 18) maps to I (position 9). Calculation: \(18 + 9 = 27\). Complementary (C).
• O (position 15) maps to L (position 12). Calculation: \(15 + 12 = 27\). Complementary (C).
• W (position 23) maps to R (position 18). Calculation: \(23 + 18 = 41\). Since \(41 \neq 27\), this is Non-complementary (N). (The complement of W is D).
• N (position 14) maps to M (position 13). Calculation: \(14 + 13 = 27\). Complementary (C).

The coding pattern for FROWN is: C, C, C, N, C. There is 1 Non-complementary mapping.

3. HAPPY : SMNMB

• H (position 8) maps to S (position 19). Calculation: \(8 + 19 = 27\). Complementary (C).
• A (position 1) maps to M (position 13). Calculation: \(1 + 13 = 14\). Since \(14 \neq 27\), this is Non-complementary (N). (The complement of A is Z).
• P (position 16) maps to N (position 14). Calculation: \(16 + 14 = 30\). Since \(30 \neq 27\), this is Non-complementary (N). (The complement of P is K).
• P (position 16) maps to M (position 13). Calculation: \(16 + 13 = 29\). Since \(29 \neq 27\), this is Non-complementary (N). (The complement of P is K).
• Y (position 25) maps to B (position 2). Calculation: \(25 + 2 = 27\). Complementary (C).

The coding pattern for HAPPY is: C, N, N, N, C. There are 3 Non-complementary mappings.

4. SNAIL : HNVRO

• S (position 19) maps to H (position 8). Calculation: \(19 + 8 = 27\). Complementary (C).
• N (position 14) maps to N (position 14). Calculation: \(14 + 14 = 28\). Since \(28 \neq 27\), this is Non-complementary (N). (The complement of N is M).
• A (position 1) maps to V (position 22). Calculation: \(1 + 22 = 23\). Since \(23 \neq 27\), this is Non-complementary (N). (The complement of A is Z).
• I (position 9) maps to R (position 18). Calculation: \(9 + 18 = 27\). Complementary (C).
• L (position 12) maps to O (position 15). Calculation: \(12 + 15 = 27\). Complementary (C).

The coding pattern for SNAIL is: C, N, N, C, C. There are 2 Non-complementary mappings.

Identifying the Odd Pair Out

Let's summarize the number of Non-complementary (N) mappings identified for each pair:

• CRUSH: 2 N's
• FROWN: 1 N
• HAPPY: 3 N's
• SNAIL: 2 N's

We observe that CRUSH, FROWN, and SNAIL have either 1 or 2 Non-complementary mappings. This suggests a common pattern where the coding relies heavily on complementary letters, with only a few exceptions.

Conversely, HAPPY: SMNMB has 3 Non-complementary mappings. This count deviates significantly from the pattern seen in the other three pairs.

Conclusion

Based on the analysis of complementary letter mappings, the pair HAPPY: SMNMB is the odd one out because it contains more non-complementary mappings compared to the others.