Concept:A pair of digits
(x,y) qualifies if the number of digits between them in the given number equals
∣x−y∣−1 (the number of digits between them in the natural numeric series
0 to
9).
Explanation:Given number:
58629371.
Position indices:
1:5,
2:8,
3:6,
4:2,
5:9,
6:3,
7:7,
8:1.
Consider unordered pairs of digits from
{5,8,6,2,9,3,7,1}.
For each pair, count the digits strictly between them in the number and compare to
∣x−y∣−1.
Pairs that satisfy the condition:
(5,6) – adjacent in both number and numeric series.
(5,2) – two digits (
8,6) between them; numeric gap
∣5−2∣−1=2.
(5,9) – three digits (
8,6,2) between them; numeric gap
∣5−9∣−1=3.
(6,9) – two digits (
8,2) between them; numeric gap
∣6−9∣−1=2.
(9,7) – one digit (
3) between them; numeric gap
∣9−7∣−1=1.
(3,1) – one digit (
7) between them; numeric gap
∣3−1∣−1=1.
No other pair satisfies the condition.
Thus, total
6 distinct pairs exist.
Answer:6 pairs, which is more than five. Hence, Option E: More than Five.