Understanding the Code Language Puzzle

The problem presents a simple substitution code language where letters are represented by digits. We are given two examples:

• 'BALD' is coded as '7680'
• 'DRAB' is coded as '8097'

We need to find the specific digit code assigned to the letter 'L' in this code language.

Analyzing the Given Code Examples

Let's list the letters in each word and the digits in their respective codes:

In a typical code language puzzle like this, each letter corresponds to a unique digit, regardless of its position in the word. The code provided is a permutation of the digits corresponding to the letters in the word.

Finding the Unique Code for 'L'

Let's identify the letters present in both words and the digits present in both codes.

• Letters common to both 'BALD' and 'DRAB': B, A, D
• Letters unique to 'BALD': L
• Letters unique to 'DRAB': R

Now, let's look at the digits in the codes:

• Digits in the code for 'BALD': {7, 6, 8, 0}
• Digits in the code for 'DRAB': {8, 0, 9, 7}

The digits that are common to both code sets must correspond to the letters that are common to both words (B, A, D).

Let's find the intersection of the two sets of digits:

\(\lbrace 7, 6, 8, 0 \rbrace \cap \lbrace 8, 0, 9, 7 \rbrace = \lbrace 7, 8, 0 \rbrace\)

So, the letters B, A, and D are coded using the digits 7, 8, and 0 in some order.

Now, consider the letter 'L'. 'L' is present only in the word 'BALD'. Its code must be a digit found in the code for 'BALD' (7680) but not found among the digits used for the common letters {B, A, D}, which are {7, 8, 0}.

• Digits in the code for 'BALD': {7, 6, 8, 0}
• Digits used for {B, A, D}: {7, 8, 0}

The digit in {7, 6, 8, 0} that is not in {7, 8, 0} is 6.

Therefore, the code for the letter 'L' is 6.

Verification (Optional)

We can apply the same logic to the letter 'R', which is unique to 'DRAB'. Its code must be a digit found in the code for 'DRAB' (8097) but not among the common digits {7, 8, 0}.

• Digits in the code for 'DRAB': {8, 0, 9, 7}
• Digits used for {B, A, D}: {7, 8, 0}

The digit in {8, 0, 9, 7} that is not in {7, 7, 0} is 9.

Therefore, the code for the letter 'R' is 9.

The letters B, A, D are coded as 7, 8, 0 in some order, L is coded as 6, and R is coded as 9. This confirms our method is consistent.

Conclusion

By identifying the unique letter in 'BALD' and finding the corresponding unique digit in its code relative to the common letters and their codes, we determined the code for 'L'.

The code for 'L' is 6.

Revision Table: Key Learnings

Additional Information: Solving Code Language Questions

Code language or coding-decoding questions are common in logical reasoning sections of competitive exams. Here are some types and tips:

• Letter-to-Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting positions in the alphabet, reverse order).
• Letter-to-Number Coding: Letters are replaced by numbers based on their alphabetical position, values assigned based on a specific rule, or as shown in this problem, arbitrary fixed mapping.
• Word-to-Word Coding: Words are replaced by other words based on a hidden logic (e.g., synonym, antonym, or a specific transformation rule).
• Tips for Solving:
• Observe the pattern carefully in the given examples.
• Compare common letters/words and their codes.
• Look for unique letters/words and their codes.
• Identify if the coding is based on position, alphabetical value, or a fixed arbitrary assignment.
• Write down the possible mappings you deduce.
• Test your deduced mapping against all given examples.

This problem used a fixed letter-to-digit mapping where the order of digits in the code did not directly correspond to the order of letters in the word, but the set of digits represented the set of letters.