Directions: Analyze the given number and answer the question that follows.

In the number ‘62947153’, how many pairs of digits have the same number of digits between them (both forward and backward directions) as they have in the standard number sequence?

The correct option is Six.

To determine the number of pairs of digits that have the same number of digits between them in the given number as in the standard number sequence (counting in both forward and backward directions), we compare the distance between their positions in the number with the difference in their numerical values.

A pair of digits at positions $i$ and $j$ with values $v_i$ and satisfies the condition if:

$|i-j|=|v_i-v_j|$

Let us write down the number 62947153 along with the 1-based position index of each digit:

• Position 1: 6
• Position 2: 2
• Position 3: 9
• Position 4: 4
• Position 5: 7
• Position 6: 1
• Position 7: 5
• Position 8: 3

Now, let us evaluate all valid pairs step-by-step:

1. Pair (6, 1):

Digit 6 is at position 1, and digit 1 is at position 6.

Position difference = $6-1=5$

Numerical difference = $6-1=5$

Since both differences are equal to 5 (meaning there are 4 digits between them in both cases), (6, 1) is a valid pair.

2. Pair (2, 4):

Digit 2 is at position 2, and digit 4 is at position 4.

Position difference = $4-2=2$

Numerical difference = $4-2=2$

Since both differences are equal to 2 (meaning there is 1 digit between them in both cases), (2, 4) is a valid pair.

3. Pair (9, 7):

Digit 9 is at position 3, and digit 7 is at position 5.

Position difference = $5-3=2$

Numerical difference = $9-7=2$

Since both differences are equal to 2 (meaning there is 1 digit between them in both cases), (9, 7) is a valid pair.

4. Pair (9, 5):

Digit 9 is at position 3, and digit 5 is at position 7.

Position difference = $7-3=4$

Numerical difference = $9-5=4$

Since both differences are equal to 4 (meaning there are 3 digits between them in both cases), (9, 5) is a valid pair.

5. Pair (7, 5):

Digit 7 is at position 5, and digit 5 is at position 7.

Position difference = $7-5=2$

Numerical difference = $7-5=2$

Since both differences are equal to 2 (meaning there is 1 digit between them in both cases), (7, 5) is a valid pair.

6. Pair (1, 3):

Digit 1 is at position 6, and digit 3 is at position 8.

Position difference = $8-6=2$

Numerical difference = $3-1=2$

Since both differences are equal to 2 (meaning there is 1 digit between them in both cases), (1, 3) is a valid pair.

Hence, there are 6 pairs of digits in total that satisfy the given condition.