In a certain code, the word 'Happiness' is written as the number sequence 517768399. Using the same letter–digit substitution, what number will represent the reversed word 'senipah'?

Introduction / Context:
In this coding–decoding question, each letter of the word Happiness is replaced by a specific digit, producing the code 517768399. We are then asked to find the code for the reversed word senipah. The key challenge is to first decode the letter–digit mapping from Happiness and then apply it to the letters of senipah in the correct order.

Given Data / Assumptions:

• Happiness is written as 517768399.
• The code represents a consistent substitution from letters to digits.
• The same mapping must be used for any other word, including senipah.
• The word senipah is simply Happiness written backwards (ignoring case).

Concept / Approach:
Since Happiness and 517768399 have equal length, each digit corresponds to one letter in the same position. We can directly read off the mapping from this pair. After learning the digit associated with each of the letters H, A, P, I, N, E and S, we reverse the letters to form senipah and substitute the corresponding digits, making sure to preserve the new order.

Step-by-Step Solution:
Step 1: Write Happiness with its letters: H A P P I N E S S. Step 2: Align the code 517768399 underneath: 5 1 7 7 6 8 3 9 9. Step 3: Extract individual mappings: H -> 5, A -> 1, P -> 7, I -> 6, N -> 8, E -> 3, S -> 9. Step 4: Confirm consistency: both P positions map to 7, both S positions map to 9, exactly as expected. Step 5: Now take the reversed word senipah (letters: S E N I P A H) and substitute digits using the mapping. Step 6: S -> 9, E -> 3, N -> 8, I -> 6, P -> 7, A -> 1, H -> 5, which gives the sequence 9 3 8 6 7 1 5. Step 7: Therefore the correct code for senipah is 9386715.

Verification / Alternative check:
We can re-check each letter carefully: S (9), E (3), N (8), I (6), P (7), A (1), H (5). All digits are taken directly from the original mapping. No digit is invented or reused incorrectly. The final sequence matches option C and fits the requirement that we simply reverse the letter order of Happiness and then apply the same digit substitution.

Why Other Options Are Wrong:
Option A: 9836715 misplaces the digits for E and N compared with our mapping. Option B: 9386615 incorrectly repeats the digit 6 instead of using 7 for P. Option D: 9386517 puts digits 1 and 7 in the wrong positions for A and P respectively. Option E: 9368715 scrambles the correct sequence and does not correspond to the proper letter order.

Common Pitfalls:
Many students forget that senipah is the reversed version of Happiness and accidentally write the digits in the original order. Others misalign letters when reading the mapping, leading to a swapped pair of digits. Carefully writing the mapping and then explicitly reversing the letters before substitution avoids these mistakes.

Final Answer:
The reversed word senipah is coded as 9386715 in this system.