In the number $83573971$, how many pairs of digits are there such that the number of digits between them (counting both forward and backward directions) is the same as the difference between the digits according to the English numeric series?

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**Solution:**

1. The number given is $8 3 5 7 3 9 7 1$.

2. We need to find pairs of digits where the count of digits between them (in either forward or backward direction) equals the absolute difference between the digits themselves.

3. Let's analyze each possible pair:

- Pair (8, 3): Difference = $|8 - 3| = 5$. Positions: 1 and 2, digits between = 0 (not equal to 5).

- Pair (8, 5): Difference = 3, positions 1 and 3, digits between = 1 (not equal).

- Pair (8, 7): Difference = 1, positions 1 and 4, digits between = 2 (not equal).

- Pair (8, 3): positions 1 and 5, difference = 5, digits between = 3 (not equal).

- Pair (8, 9): positions 1 and 6, difference = 1, digits between = 4 (not equal).

- Pair (8, 7): positions 1 and 7, difference = 1, digits between = 5 (not equal).

- Pair (8, 1): positions 1 and 8, difference = 7, digits between = 6 (not equal).

- Pair (3, 5): difference = 2, positions 2 and 3, digits between = 0 (not equal).

- Pair (3, 7): difference = 4, positions 2 and 4, digits between = 1 (not equal).

- Pair (3, 3): difference = 0, positions 2 and 5, digits between = 2 (not equal).

- Pair (3, 9): difference = 6, positions 2 and 6, digits between = 3 (not equal).

- Pair (3, 7): difference = 4, positions 2 and 7, digits between = 4 (equal) → **Valid Pair 1**

- Pair (3, 1): difference = 2, positions 2 and 8, digits between = 5 (not equal).

- Pair (5, 7): difference = 2, positions 3 and 4, digits between = 0 (not equal).

- Pair (5, 3): difference = 2, positions 3 and 5, digits between = 1 (not equal).

- Pair (5, 9): difference = 4, positions 3 and 6, digits between = 2 (not equal).

- Pair (5, 7): difference = 2, positions 3 and 7, digits between = 3 (not equal).

- Pair (5, 1): difference = 4, positions 3 and 8, digits between = 4 (equal) → **Valid Pair 2**

- Pair (7, 3): difference = 4, positions 4 and 5, digits between = 0 (not equal).

- Pair (7, 9): difference = 2, positions 4 and 6, digits between = 1 (not equal).

- Pair (7, 7): difference = 0, positions 4 and 7, digits between = 2 (not equal).

- Pair (7, 1): difference = 6, positions 4 and 8, digits between = 3 (not equal).

- Pair (3, 9): difference = 6, positions 5 and 6, digits between = 0 (not equal).

- Pair (3, 7): difference = 4, positions 5 and 7, digits between = 1 (not equal).

- Pair (3, 1): difference = 2, positions 5 and 8, digits between = 2 (equal) → **Valid Pair 3**

- Pair (9, 7): difference = 2, positions 6 and 7, digits between = 0 (not equal).

- Pair (9, 1): difference = 8, positions 6 and 8, digits between = 1 (not equal).

- Pair (7, 1): difference = 6, positions 7 and 8, digits between = 0 (not equal).

4. We find exactly **3** such pairs.

**Answer:** Three

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