Decoding the Coding Pattern for TAIL and TALE

This problem presents a coding challenge where words are assigned numerical codes. We are given two examples:

• The word 'TAIL' is coded as '7614'.
• The word 'TALE' is coded as '1749'.

Our objective is to determine the specific numerical code assigned to the letter 'I' within this coding system.

Comparing Word Codes to Find Letter Values

To crack this code, we will compare the two given words and their numerical representations. This comparison helps us identify which numbers correspond to which letters. Let's list the components:

Identifying Common and Unique Elements

By comparing the letters present in both 'TAIL' and 'TALE', and the digits used in their respective codes, we can make logical deductions:

• Common Letters: Both 'TAIL' and 'TALE' contain the letters T, A, and L.
• Common Digits: The codes '7614' and '1749' share the digits 7, 1, and 4.

This implies that the set of common letters {T, A, L} corresponds to the set of common digits {1, 4, 7}. Each of these letters is assigned one of these digits, though the order might vary.

Deducing Codes for Unique Letters

Next, we examine the letters and digits that are unique to each word-code pair:

• The letter 'I' appears in 'TAIL' but not in 'TALE'. Correspondingly, the digit '6' appears in the code '7614' but not in '1749'.
• The letter 'E' appears in 'TALE' but not in 'TAIL'. Correspondingly, the digit '9' appears in the code '1749' but not in '7614'.

Based on this unique correspondence, we can directly conclude:

• The code for the letter 'I' is 6.
• The code for the letter 'E' is 9.

Final Determination of the Code for 'I'

Summarizing our findings:

• The letters T, A, and L are represented by the digits 1, 4, and 7 (in some order).
• The letter 'I' is uniquely associated with the digit 6.
• The letter 'E' is uniquely associated with the digit 9.

Therefore, the code for the letter 'I' in this given language is 6.