Concept:A pair of digits is counted if the number of digits between them in the given number is the same as the number of digits between them in the natural number sequence.
Explanation:Write the number with their positions from left to right:
Number:
3 9 4 7 2 8 1 6Positions:
1 2 3 4 5 6 7 8For any two digits at positions
p and
q, the required condition is:
∣p−q∣=∣dp−dq∣This covers both forward and backward counting, since the number of digits between the pair is the same in either direction.
Now check all possible pairs:
4 and
2: positions
3 and
5 ⇒∣3−5∣=2, values
∣4−2∣=2 ✔
3 and
8: positions
1 and
6 ⇒∣1−6∣=5, values
∣3−8∣=5 ✔
6 and
8: positions
8 and
6 ⇒∣8−6∣=2, values
∣6−8∣=2 ✔
7 and
9: positions
4 and
2 ⇒∣4−2∣=2, values
∣7−9∣=2 ✔
Hence, there are 4 such pairs, which is more than three.
Answer:More than three (Option E).
