Understanding the Coding-Decoding Pattern

This question involves a coding-decoding puzzle where words are converted into numerical codes based on a specific pattern or rule. We are given two examples:

• 'BOSS' is coded as '21967'
• 'DEAL' is coded as '19192414'

Our goal is to determine the code for the word 'GAIN' using the same logic.

Analyzing the Given Codes

Let's look at the letters and their positions in the standard English alphabet (A=1, B=2, ..., Z=26).

• BOSS: B(2), O(15), S(19), S(19) -> Code: 21967 (5 digits)
• DEAL: D(4), E(5), A(1), L(12) -> Code: 19192414 (8 digits)

The number of digits in the codes is different for words of the same length (4 letters). This suggests the coding isn't a simple concatenation of standard alphabetical positions.

Let's examine the second example, 'DEAL', more closely as its code '19192414' seems to split nicely into four two-digit numbers: 19, 19, 24, 14. If each letter is coded as a two-digit number:

• D -> 19
• E -> 19
• A -> 24
• L -> 14

Comparing this with the standard positions (D=4, E=5, A=1, L=12) or their reverse positions (D=23, E=22, A=26, L=15) doesn't reveal a simple arithmetic operation.

Discovering the Coding Logic

Let's look at the reverse alphabetical positions. The reverse position of a letter is calculated as $\text{Reverse Position} = 27 - \text{Alphabetical Position}$.

• DEAL:
• D: Standard 4, Reverse 27-4 = 23. Code 19. Difference: 23 - 19 = 4.
• E: Standard 5, Reverse 27-5 = 22. Code 19. Difference: 22 - 19 = 3.
• A: Standard 1, Reverse 27-1 = 26. Code 24. Difference: 26 - 24 = 2.
• L: Standard 12, Reverse 27-12 = 15. Code 14. Difference: 15 - 14 = 1.

A pattern emerges: for a 4-letter word, the code for each letter is its reverse alphabetical position minus a decreasing sequence of numbers (4, 3, 2, 1).

Let's test this logic with 'BOSS'. It's also a 4-letter word (N=4), so the subtraction sequence should be 4, 3, 2, 1.

• BOSS:
• B: Standard 2, Reverse 27-2 = 25. Subtract 4: 25 - 4 = 21.
• O: Standard 15, Reverse 27-15 = 12. Subtract 3: 12 - 3 = 9.
• S: Standard 19, Reverse 27-19 = 8. Subtract 2: 8 - 2 = 6.
• S: Standard 19, Reverse 27-19 = 8. Subtract 1: 8 - 1 = 7.

Concatenating these results (21, 9, 6, 7) gives '21967', which matches the code for 'BOSS'. The logic holds true for both examples.

Coding the Word 'GAIN'

'GAIN' is a 4-letter word (N=4), so we will use the same pattern: find the reverse alphabetical position of each letter and subtract 4, 3, 2, and 1 respectively.

• G: Standard 7, Reverse 27-7 = 20. Subtract 4: 20 - 4 = 16.
• A: Standard 1, Reverse 27-1 = 26. Subtract 3: 26 - 3 = 23.
• I: Standard 9, Reverse 27-9 = 18. Subtract 2: 18 - 2 = 16.
• N: Standard 14, Reverse 27-14 = 13. Subtract 1: 13 - 1 = 12.

Concatenating the resulting numbers gives the code for 'GAIN': 16231612.

Comparing with Options

Let's compare our calculated code with the given options:

1. 16231512
2. 16241612
3. 16231612
4. 16231611

Our calculated code '16231612' matches Option 3.

Revision Table: Coding Logic Summary

Additional Information: Types of Coding-Decoding

Coding-decoding questions are common in logical reasoning tests. They assess your ability to identify patterns and rules. Common types include:

• Letter Coding: Letters are substituted by other letters based on a pattern (e.g., shifting position in the alphabet).
• Number Coding: Words are coded into numbers. This can be based on alphabetical position, reverse position, number of letters, vowel/consonant counts, or complex arithmetic operations as seen in this problem.
• Symbol Coding: Letters or words are coded using symbols.
• Mixed Coding: Words, numbers, and symbols are all used in the coding.
• Substitution: One word is substituted for another (e.g., 'red' is called 'blue', 'blue' is called 'green').

Solving these questions requires careful observation, pattern identification, and systematic application of the logic derived from the examples.