Digit swap in positions – For the number 83721569, interchange (1↔5), (2↔6), (3↔7), and (4↔8). After rearrangement, which digit is third from the right end?

Introduction / Context:
The problem requires performing specified index swaps and then reading an element at a given position from the right end.

Given Data / Assumptions:

• Original digits (1-based): [8,3,7,2,1,5,6,9].
• Swap pairs: (1,5), (2,6), (3,7), (4,8).

Concept / Approach:
Apply swaps carefully; then map “third from right” to the 6th position from the left in an 8-digit number (since 8 - 3 + 1 = 6).

Step-by-Step Solution:
After swaps: pos1=1, pos2=5, pos3=6, pos4=9, pos5=8, pos6=3, pos7=7, pos8=2.Third from the right = position 6 = 3.

Verification / Alternative check:
Right indexing: rightmost (1st)→2, 2nd→7, 3rd→3. Confirms the value 3.

Why Other Options Are Wrong:
6/2/7 occur at other positions but not third from right after the prescribed swaps.

Common Pitfalls:
Performing swaps sequentially but reusing updated values incorrectly; here each pair is a direct swap of original positions.

Final Answer:
3