Understanding the Code Language Problem

This question asks us to find the code assigned to the letter 'R' based on the given information about a specific code language. We are given two coded words: 'PYRE' is coded as '5108' and 'YELP' is coded as '8601'. These types of problems usually involve a substitution cipher, where each letter corresponds to a specific digit.

Analyzing the Given Codes

Let's look at the letters in each word and the digits in their corresponding codes:

• Word 1: PYRE, Code: 5108
• Word 2: YELP, Code: 8601

The letters involved are P, Y, R, E (from PYRE) and Y, E, L, P (from YELP). The digits involved are 5, 1, 0, 8 (from 5108) and 8, 6, 0, 1 (from 8601).

Finding the Code for 'R'

To find the code for 'R', we should compare the two words and their codes. Let's identify the letters and digits that are unique to each word/code and those that are common.

Common Elements:

• Letters common to both words: Y, E, P
• Digits common to both codes (5108 and 8601): 1, 0, 8

This suggests that the letters Y, E, and P are coded using the digits 1, 0, and 8, although we don't know the exact mapping yet just from the common elements.

Unique Elements:

• Letter unique to 'PYRE' (not in 'YELP'): R
• Letter unique to 'YELP' (not in 'PYRE'): L

Now let's look at the codes:

• Digits in '5108' that are unique compared to '8601': 5
• Digits in '8601' that are unique compared to '5108': 6

This is the key observation. The letter 'R' appears only in 'PYRE', and the digit '5' appears only in the code '5108'. Similarly, the letter 'L' appears only in 'YELP', and the digit '6' appears only in the code '8601'. This strongly indicates a direct mapping between the unique letter and the unique digit in each pair.

Therefore, based on this pattern:

• The letter R is coded as the digit 5.
• The letter L is coded as the digit 6.

The remaining common letters {Y, E, P} must be coded by the remaining common digits {1, 0, 8}. We can even deduce further mappings, but the question only asks for the code of 'R'.

• From PYRE (5108): If P=5, Y,R,E must map to 1,0,8. But we found R=5, this would be a conflict. This means the order of letters doesn't strictly match the order of digits.
• It's a simple substitution: each letter has a unique digit code.
• PYRE = 5108 means P, Y, R, E are coded as 5, 1, 0, 8 in some order.
• YELP = 8601 means Y, E, L, P are coded as 8, 6, 0, 1 in some order.
• Comparing the sets of letters {P, Y, R, E} and {Y, E, L, P}, the unique letters are R and L.
• Comparing the sets of digits {5, 1, 0, 8} and {8, 6, 0, 1}, the unique digits are 5 and 6.
• Thus, R must correspond to 5, and L must correspond to 6.

The code for 'R' is 5.

Conclusion

Based on the analysis of unique letters and digits in the given coded words, the code for 'R' is determined to be 5.

This confirms that R is coded as 5.

Revision Table - Code Language Analysis

Additional Information - Types of Coding Questions

Coding-decoding questions in competitive exams often involve different patterns:

• Letter Shifting: Letters are shifted a certain number of places forward or backward in the alphabet (e.g., A becomes C, B becomes D, etc.).
• Direct Letter Substitution: Each letter is replaced by another specific letter or symbol/digit, regardless of position. This is the type seen in this problem.
• Position-Based Coding: The code depends on the position of the letter in the word (e.g., 1st letter gets code X, 2nd letter gets code Y, regardless of the letter itself). This was initially considered but ruled out based on the conflicting codes for P and Y.
• Mixed Coding: A combination of the above rules.
• Word-to-Word Coding: Entire words are replaced by other words based on a hidden logic.

For direct substitution problems like this one, comparing multiple examples with common and unique elements is a very effective strategy.