How many pairs of digits are there in the number $59267435$, such that the number of digits between them in the number (considering both forward and backward directions) is equal to the number of digits between them in the natural numeric series?

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**Solution:**

1. The number given is $59267435$. We need to find pairs of digits where the count of digits between them in the number matches the count of digits between them in the natural numeric series.

2. First, understand the numeric series: digits $0$ through $9$ in order.

3. For each pair of digits in the number, calculate:
   - The number of digits between them in the number (both forward and backward directions).
   - The number of digits between them in the numeric series.

4. Check if these two counts are equal.

5. Let's analyze pairs:

- Pair (5, 9): Positions 1 and 2 in the number.
     - Digits between in number: 0 (adjacent)
     - Digits between in series: digits between 5 and 9 are 6,7,8 → 3 digits
     - Not equal.

- Pair (9, 2): Positions 2 and 3.
     - Digits between in number: 0
     - Digits between in series: digits between 2 and 9 are 3,4,5,6,7,8 → 6 digits
     - Not equal.

- Pair (5, 2): Positions 1 and 3.
     - Digits between in number: 1 (digit 9)
     - Digits between in series: digits between 2 and 5 are 3,4 → 2 digits
     - Not equal.

- Pair (9, 6): Positions 2 and 5.
     - Digits between in number: digits at positions 3 and 4 → 2 digits
     - Digits between in series: digits between 6 and 9 are 7,8 → 2 digits
     - Equal → 1 pair.

- Pair (2, 7): Positions 3 and 4.
     - Digits between in number: 0
     - Digits between in series: digits between 2 and 7 are 3,4,5,6 → 4 digits
     - Not equal.

- Pair (7, 4): Positions 4 and 6.
     - Digits between in number: digit at position 5 → 1 digit
     - Digits between in series: digits between 4 and 7 are 5,6 → 2 digits
     - Not equal.

- Pair (6, 4): Positions 5 and 6.
     - Digits between in number: 0
     - Digits between in series: digits between 4 and 6 is 5 → 1 digit
     - Not equal.

- Pair (4, 3): Positions 6 and 7.
     - Digits between in number: 0
     - Digits between in series: digits between 3 and 4 is none → 0 digits
     - Equal → 2 pairs.

- Pair (3, 5): Positions 7 and 8.
     - Digits between in number: 0
     - Digits between in series: digits between 3 and 5 is 4 → 1 digit
     - Not equal.

- Pair (2, 6): Positions 3 and 5.
     - Digits between in number: digit at position 4 → 1 digit
     - Digits between in series: digits between 2 and 6 are 3,4,5 → 3 digits
     - Not equal.

- Pair (5, 7): Positions 1 and 4.
     - Digits between in number: digits at positions 2 and 3 → 2 digits
     - Digits between in series: digits between 5 and 7 is 6 → 1 digit
     - Not equal.

- Pair (9, 7): Positions 2 and 4.
     - Digits between in number: digit at position 3 → 1 digit
     - Digits between in series: digits between 7 and 9 is 8 → 1 digit
     - Equal → 3 pairs.

- Pair (7, 5): Positions 4 and 8.
     - Digits between in number: digits at positions 5,6,7 → 3 digits
     - Digits between in series: digits between 5 and 7 is 6 → 1 digit
     - Not equal.

- Pair (6, 3): Positions 5 and 7.
     - Digits between in number: digit at position 6 → 1 digit
     - Digits between in series: digits between 3 and 6 are 4,5 → 2 digits
     - Not equal.

6. Counting all pairs that satisfy the condition, we get 4 pairs.

**Answer:** (d) Four

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