Understanding the Coding Pattern

This problem is about deciphering a simple substitution code where letters are represented by numbers. We are given two examples:

• The word 'DEAL' is coded as '7298'.
• The word 'APEL' is coded as '2678'.

Our task is to determine the specific numerical code for the letter 'P' based on these examples.

Step-by-Step Solution

Step 1: List the Given Codes

Let's write down the provided information clearly:

Step 2: Compare the Words and Codes

To find the code for 'P', we need to compare the two given word-code pairs.

Common elements:

• Letters common to both 'DEAL' and 'APEL' are: A, E, L.
• Digits common to both codes '7298' and '2678' are: 2, 7, 8.

This comparison suggests that the letters {A, E, L} correspond to the digits {2, 7, 8} in some order.

Step 3: Identify Unique Elements

Now, let's look for elements unique to each pair:

• The word 'DEAL' has the letter 'D' which is not in 'APEL'. Its code '7298' has the digit '9' which is not in the code '2678'. This implies a direct correspondence: D = 9.
• The word 'APEL' has the letter 'P' which is not in 'DEAL'. Its code '2678' has the digit '6' which is not in the code '7298'. This implies a direct correspondence: P = 6.

Step 4: Determine the Code for 'P'

Based on the analysis of unique elements in Step 3, we identified that the unique letter 'P' in 'APEL' corresponds to the unique digit '6' in its code '2678'.

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

Final Answer Summary

By comparing the common and unique letters and digits between the coded words 'DEAL' (7298) and 'APEL' (2678), we can deduce the code for individual letters. The letter 'P' appears only in 'APEL', and the digit '6' appears only in the code '2678'. This establishes the code for 'P' as 6.

The code for 'P' is 6.