In the number 2796543018, the positions of the first and sixth digits are interchanged, the positions of the second and seventh digits are interchanged, and so on in the same pattern. After this rearrangement, which of the following digits will be the seventh digit from the left end?

Introduction / Context:
This problem is similar to the previous digit swapping question but with a different original number. It involves a structured interchange of digit positions in a ten digit number and then asks for the digit at a specific position after the rearrangement. The question tests careful application of the described swapping pattern and accurate reading of positions from the left.

Given Data / Assumptions:

• Original number: 2796543018.
• Digits are initially in positions 1 to 10 from left to right.
• Positions swapped are (1,6), (2,7), (3,8), (4,9) and (5,10).
• We must find the digit that becomes the seventh digit from the left end after all swaps.

Concept / Approach:
To solve such digit interchange problems, it is important to label each position and digit clearly, then apply each swap exactly once. After all swaps are completed, the final arrangement can be written down, and the requested digit can be identified by counting from the left. Systematic recording of each step avoids confusion and prevents accidental double swapping.

Step-by-Step Solution:
Step 1: Label the original digits with positions from left to right: 1:2, 2:7, 3:9, 4:6, 5:5, 6:4, 7:3, 8:0, 9:1, 10:8. Step 2: Swap positions 1 and 6. The digits 2 and 4 interchange. New positions: 1:4, 2:7, 3:9, 4:6, 5:5, 6:2, 7:3, 8:0, 9:1, 10:8. Step 3: Swap positions 2 and 7. Digits 7 and 3 interchange. New positions: 1:4, 2:3, 3:9, 4:6, 5:5, 6:2, 7:7, 8:0, 9:1, 10:8. Step 4: Swap positions 3 and 8. Digits 9 and 0 interchange. New positions: 1:4, 2:3, 3:0, 4:6, 5:5, 6:2, 7:7, 8:9, 9:1, 10:8. Step 5: Swap positions 4 and 9. Digits 6 and 1 interchange. New positions: 1:4, 2:3, 3:0, 4:1, 5:5, 6:2, 7:7, 8:9, 9:6, 10:8. Step 6: Swap positions 5 and 10. Digits 5 and 8 interchange. Final positions: 1:4, 2:3, 3:0, 4:1, 5:8, 6:2, 7:7, 8:9, 9:6, 10:5. Step 7: The final number is 4301827965. Step 8: Count digits from the left: positions are 1:4, 2:3, 3:0, 4:1, 5:8, 6:2, 7:7, 8:9, 9:6, 10:5. Step 9: The seventh digit from the left is 7.

Verification / Alternative check:
Rewriting the final sequence and checking the position again confirms that after all swaps the digit at position 7 is 7. None of the swaps affect the fact that the seventh position is reached after counting exactly six digits to its left, and the only digit at that position in the final arrangement is 7.

Why Other Options Are Wrong:
Digits 1, 0 and 8 all appear in the final number but not at the seventh position. They occupy other positions from the left.

Common Pitfalls:
Errors commonly arise from mislabeling the initial positions or performing the swaps out of order. Some students may also misread the question and look for the seventh digit from the right instead of from the left. A clear table of positions and careful counting from the left helps avoid these mistakes.

Final Answer:
The seventh digit from the left after the rearrangement is 7.