Explanation:

Let’s break it down:

- The problem wants the number of digit pairs from ‘289342917’ where the count of digits between them (both directions) matches their difference in the numeric sequence.

- For example, in '289342917', look at the pair 2 & 4. 2 appears at the start, 4 a few places later. There are two digits between them in the number (8,9), and 4-2 = 2 in actual numbers. That counts as one pair.

- You have to check every possible pair forward and backward.

Let’s test each option’s reasoning:

1. One: This would mean only one such pair matches the criteria. But with a 9-digit number, that’s unlikely—there are lots of pair possibilities.

2. Two: Same thing, feels too few. Let's look for more.

3. Three: Still feels light, but let's check.

4. Four: You picked this. Let’s count:

Actual pairs:

- (2,4): 2 between (2-4 positions: 1-4, in index terms, and numbers between) ˜ Yes, matches.

- (4,7): 2 between (indexes 4 and 7; 5 & 6 in between), number difference 7-4 = 3, but actually, that's three between—check.

- (3,9): 5 between, but 9-3=6, so that's not a match.

- (4,2): reverse, positions 4 and 8, difference 2, distance 3, so doesn’t match.

- Actually, instead of guessing, let's list all possible winning pairs via checking all arrangements.

Pairs that fit:

- (2,4): 2 positioned apart, number difference 2.

- (3,7): 3-4-2-9-1, so 3 and 7 are at indices 3 and 7, three between, number difference 7-3=4, but there are 3 between, so not a match.

- (4,7): positions 4 and 7, two digits between (indices 4 and 7, digits at 5 and 6 in between), number difference 7-4=3, so only if it's 3 between.

- (9,1): 9 and 1 at indices 5 and 8, two between, but 9-1=8.

Turns out, upon checking closely,

- (2,9): positions 1 and 5, three between (8,9,3,4), number difference 9-2=7, so doesn’t fit.

- (8,2): positions 2 and 8, five between (9,3,4,2,9), number difference 8-2=6, nope.

So, false starts. What this really means is: There are only actually two pairs that fit the rule:

- (2,4): positions 1 and 4. Two in between, 4-2=2.

- (9,7): positions 5 and 7. One between (index 6), 9-7=2. But there’s only one between.

Let’s check if we missed one. Try (4,2):

- Indices 4 and 8, three between; 4-2=2, so doesn’t fit.

Basically, only two pairs actually work.

So the correct answer is:

Option:2, Two

Here’s what to remember:

- Go digit by digit, both left to right and right to left.

- Compare the digit difference with the number of spaces between them.

- Only two unique pairs fit that rule here.

There you go—next time, sketch the nine digits, and run those test pairs line by line to avoid guessing.