Understanding the Coding Logic for Letters

This problem involves figuring out a pattern where specific letters are represented by numerical codes. We are given two examples: 'PANT' is coded as '6129' and 'TAPE' is coded as '2956'. Our task is to determine the code for the letter 'E' based on this pattern.

Analyzing the Provided Codes

Let's clearly lay out the information given:

• Word 1: PANT corresponds to the code 6129
• Word 2: TAPE corresponds to the code 2956

Identifying Letter-to-Number Mappings

To crack this code, we need to compare the letters present in the words and the digits used in their respective codes. We can find the code for 'E' by looking at the letters and digits that are unique to one word/code pair compared to the other.

Comparing Common Letters and Digits:

• The letters common to both 'PANT' and 'TAPE' are 'P', 'A', and 'T'.
• The digits used in the code for 'PANT' (6129) are the set {6, 1, 2, 9}.
• The digits used in the code for 'TAPE' (2956) are the set {2, 9, 5, 6}.
• By comparing these sets, we see that the digits {2, 6, 9} appear in both codes. This suggests that the letters 'P', 'A', and 'T' are likely represented by these digits {2, 6, 9}, although we don't know the exact mapping for each yet.

Identifying Unique Letters and Digits:

Let's focus on the letters that appear in only one word and the digits that appear in only one code:

• The letter 'N' appears only in the word 'PANT'.
• Comparing the digit sets, the digit '1' is present in the code for 'PANT' (6129) but is absent in the code for 'TAPE' (2956).
• Since 'N' is the unique letter in 'PANT' and '1' is the unique digit in its code (relative to the other word's code), it's logical to conclude that the code for 'N' is 1.

Similarly, let's consider the word 'TAPE':

• The letter 'E' appears only in the word 'TAPE'.
• Comparing the digit sets again, the digit '5' is present in the code for 'TAPE' (2956) but is absent in the code for 'PANT' (6129).
• Because 'E' is the unique letter in 'TAPE' and '5' is the unique digit in its corresponding code (relative to the other word's code), we can deduce that the code for 'E' is 5.

Determining the Code for 'E'

Our analysis shows a clear pattern:

• N (unique to PANT) maps to 1 (unique digit in PANT's code).
• E (unique to TAPE) maps to 5 (unique digit in TAPE's code).

Therefore, the code for the letter 'E' is 5.