In a certain code language, ‘RUIN' is coded as '3719' and 'RUNG' is coded as '7916'. What is the code for 'G' in the given code language?
6
Coding Logic Explained
This problem involves deciphering a simple substitution code where letters are represented by numbers. We are given two examples of coded words and need to find the code for a specific letter.
Problem Statement
- The word 'RUIN' is coded as '3719'.
- The word 'RUNG' is coded as '7916'.
- We need to find the code for the letter 'G'.
Letter-to-Code Mappings Analysis
To solve this, we need to compare the given words and their codes to identify patterns. Let's list the letters and their corresponding digits for each word:
| Letter | R | U | I | N |
|---|---|---|---|---|
| Code Digits | 3 | 7 | 1 | 9 |
| Letter | R | U | N | G |
|---|---|---|---|---|
| Code Digits | 7 | 9 | 1 | 6 |
Common and Unique Elements
Let's compare the letters present in both words and the digits used in their codes:
- Common Letters: Both 'RUIN' and 'RUNG' contain the letters 'R', 'U', and 'N'.
- Common Digits in Codes: The codes '3719' and '7916' share the digits '7', '9', and '1'. This suggests that the letters 'R', 'U', and 'N' are collectively represented by the digits '7', '9', and '1' in some order.
Code Deduction for 'G'
Now, let's look for unique elements:
- In the word 'RUIN', the letters are R, U, I, N and the code is 3719. The set of digits is {3, 7, 1, 9}.
- In the word 'RUNG', the letters are R, U, N, G and the code is 7916. The set of digits is {7, 9, 1, 6}.
- We established that the common letters {R, U, N} correspond to the common digits {7, 9, 1}.
- The letter unique to 'RUIN' is 'I'. The digit unique to the code '3719' (when compared to the digits in '7916') is '3'. Therefore, we can deduce that I = 3.
- The letter unique to 'RUNG' is 'G'. The digit unique to the code '7916' (when compared to the digits in '3719') is '6'. Therefore, we can deduce that G = 6.
Code for G Answer
Based on the analysis, the letter 'G' corresponds to the digit '6' in this coding language. This is found by identifying the digit present in the code for 'RUNG' (7916) that is not present in the code for 'RUIN' (3719), and matching it with the letter unique to 'RUNG' that is not present in 'RUIN'.
The code for 'G' is 6.
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