Understanding the Coding Pattern

The problem presents a coding language where words are represented by numbers. We are given two examples: 'CARD' is coded as '6135' and 'DRAW' is coded as '1765'. We need to find the code for the letter 'W'.

Identifying Common and Unique Elements

To solve this, we compare the letters and digits in both given codes:

• Word 1: CARD = 6135
• Word 2: DRAW = 1765

Let's analyze the commonalities and differences:

• Common Letters: The letters 'A', 'R', and 'D' appear in both 'CARD' and 'DRAW'.
• Common Digits: The digits '1', '6', and '5' appear in both codes '6135' and '1765'.
• This suggests that the common letters {A, R, D} correspond to the common digits {1, 6, 5} in some fixed mapping.

Determining the Code for 'W'

Now, let's look at the unique elements:

• Unique Letter in CARD: 'C'. The digit '3' appears in '6135' but not in '1765'.
• Unique Letter in DRAW: 'W'. The digit '7' appears in '1765' but not in '6135'.

Based on this observation, we can establish the following mappings:

• The unique letter 'C' corresponds to the unique digit '3'. So, C = 3.
• The unique letter 'W' corresponds to the unique digit '7'. So, W = 7.

The question specifically asks for the code for 'W'. Therefore, the code for 'W' is 7.