How many pair of digits are in the number ‘271384569’, each of which have as many digits between them as in number series (both forward and backward direction)?

The correct answer is More than four.

To find the pairs of digits in the number 271384569 that have the same number of digits between them as in the standard numerical series (in both forward and backward directions), we analyze the position of each digit relative to the others.

Let's write down the digits with their corresponding positions (1-indexed from left to right):
Digit: 2 (Pos 1)
Digit: 7 (Pos 2)
Digit: 1 (Pos 3)
Digit: 3 (Pos 4)
Digit: 8 (Pos 5)
Digit: 4 (Pos 6)
Digit: 5 (Pos 7)
Digit: 6 (Pos 8)
Digit: 9 (Pos 9)

A pair of digits (a, b) at positions (i, j) with i < j qualifies if the absolute difference between the digits equals the difference between their positions. That is:
$|a-b|=j-i$

Let's check the pairs systematically:

1. Pair (2, 3):
Digit 2 is at position 1, and digit 3 is at position 4.
Difference between digits: $3-2=1$
Difference between positions: $4-1=3$ (Not a match)

2. Pair (7, 8):
Digit 7 is at position 2, and digit 8 is at position 5.
Difference between digits: $8-7=1$
Difference between positions: $5-2=3$ (Not a match)

3. Pair (1, 3):
Digit 1 is at position 3, and digit 3 is at position 4.
Difference between digits: $3-1=2$
Difference between positions: $4-3=1$ (Not a match)

4. Pair (1, 4):
Digit 1 is at position 3, and digit 4 is at position 6.
Difference between digits: $4-1=3$
Difference between positions: $6-3=3$ (Matches! There are 3 numbers in the series between 1 and 4, i.e., 2, 3, and there are 2 digits between them in the number: 3, 8)
First Pair: (1, 4)

5. Pair (1, 5):
Digit 1 is at position 3, and digit 5 is at position 7.
Difference between digits: $5-1=4$
Difference between positions: $7-3=4$ (Matches!)
Second Pair: (1, 5)

6. Pair (1, 6):
Digit 1 is at position 3, and digit 6 is at position 8.
Difference between digits: $6-1=5$
Difference between positions: $8-3=5$ (Matches!)
Third Pair: (1, 6)

7. Pair (3, 4):
Digit 3 is at position 4, and digit 4 is at position 6.
Difference between digits: $4-3=1$
Difference between positions: $6-4=2$ (Not a match)

8. Pair (3, 5):
Digit 3 is at position 4, and digit 5 is at position 7.
Difference between digits: $5-3=2$
Difference between positions: $7-4=3$ (Not a match)

9. Pair (3, 6):
Digit 3 is at position 4, and digit 6 is at position 8.
Difference between digits: $6-3=3$
Difference between positions: $8-4=4$ (Not a match)

10. Pair (8, 9):
Digit 8 is at position 5, and digit 9 is at position 9.
Difference between digits: $9-8=1$
Difference between positions: $9-5=4$ (Not a match)

11. Pair (4, 5):
Digit 4 is at position 6, and digit 5 is at position 7.
Difference between digits: $5-4=1$
Difference between positions: $7-6=1$ (Matches!)
Fourth Pair: (4, 5)

12. Pair (4, 6):
Digit 4 is at position 6, and digit 6 is at position 8.
Difference between digits: $6-4=2$
Difference between positions: $8-6=2$ (Matches!)
Fifth Pair: (4, 6)

13. Pair (5, 6):
Digit 5 is at position 7, and digit 6 is at position 8.
Difference between digits: $6-5=1$
Difference between positions: $8-7=1$ (Matches!)
Sixth Pair: (5, 6)

14. Pair (7, 9):
Digit 7 is at position 2, and digit 9 is at position 9.
Difference between digits: $9-7=2$
Difference between positions: $9-2=7$ (Not a match)

Since we have found at least 6 valid pairs (which are (1, 4), (1, 5), (1, 6), (4, 5), (4, 6), and (5, 6)), the total count of such pairs is more than four.