Digit arrangement – Swap positions (1↔6, 2↔7, 3↔8, 4↔9, 5↔10) in the 10-digit string 5904627813. After this paired swap, which digit is fourth from the right end?

Difficulty: Medium

Correct Answer: 9

Explanation:


Introduction / Context:
This problem tests careful indexing and stable, pairwise swaps. We take the 10-digit sequence 5904627813 and swap positions in fixed pairs: (1↔6), (2↔7), (3↔8), (4↔9), (5↔10). Then we must read the fourth digit from the right of the resulting string.


Given Data / Assumptions:

  • Original string (left→right positions 1..10): 5 9 0 4 6 2 7 8 1 3
  • Swaps: (1,6), (2,7), (3,8), (4,9), (5,10).
  • After swaps, read the 4th digit from the right (i.e., position 7 from the left).


Concept / Approach:
Perform the swaps carefully without cascading errors (treat swaps as simultaneous or track in a copy). After the final arrangement, identify the 4th from right. Alternatively, compute that “4th from right” equals index 10−4+1 = 7 from the left.


Step-by-Step Solution:

Write indices: 1:5, 2:9, 3:0, 4:4, 5:6, 6:2, 7:7, 8:8, 9:1, 10:3.Swap (1,6): positions 1↔6 → 2 at pos1, 5 at pos6.Swap (2,7): positions 2↔7 → 7 at pos2, 9 at pos7.Swap (3,8): positions 3↔8 → 8 at pos3, 0 at pos8.Swap (4,9): positions 4↔9 → 1 at pos4, 4 at pos9.Swap (5,10): positions 5↔10 → 3 at pos5, 6 at pos10.Final sequence (1..10): 2 7 8 1 3 5 9 0 4 6.Fourth from right = index 7 from left = digit 9.


Verification / Alternative check:
Count from the right: (1)6, (2)4, (3)0, (4)9 → same result.


Why Other Options Are Wrong:

  • 4, 1, 0: Appear in the final string but not at the 4th-from-right position.
  • None of these: There is a correct listed option (9).


Common Pitfalls:
Applying swaps in-place in a way that uses already-swapped values; miscounting “4th from right”; or indexing from zero. Work with a copied array or treat swaps as simultaneous.


Final Answer:
9

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