A coding scheme assigns numerical values to letters based on their alphabetical positions (A=1, B=2, C=3, ..., Z=26). For example, HAT = 29. Using the same letter-position sum method, what is the value of PAN?

Introduction / Context:
This question uses the standard alphabet-position coding system where each letter is replaced by its position in the alphabet, and the word value is the sum of those positions. You must apply the same method to a new word.

Given Data / Assumptions:

• A=1, B=2, ..., Z=26.
• Example: HAT = 29.
• Find PAN using the same rule (sum of letter positions).

Concept / Approach:
Convert each letter in the word to its alphabetical position and add them. Validate the rule using HAT to confirm that the interpretation is correct.

Step-by-Step Solution:
First verify HAT: H = 8, A = 1, T = 20 Sum = 8 + 1 + 20 = 29 (matches). Now compute PAN: P = 16 A = 1 N = 14 Sum = 16 + 1 + 14 = 31

Verification / Alternative check:
A quick mental check: P(16) and N(14) already total 30, plus A(1) gives 31. This is consistent with the same method used for HAT.

Why Other Options Are Wrong:
28: would occur if N is mistaken as 11 or if a letter is skipped. 21: could come from counting letters rather than positions. 41: often from using A=0 or adding extra offsets incorrectly. 33: from misreading P as 18 or N as 16.

Common Pitfalls:
Using A=0, confusing letter positions, or applying reverse positions (A=26) instead of forward positions are common errors.

Final Answer:
31