How many pairs of digits are there in the number 48261539 that have the same number of digits between them as in the standard numerical sequence (in both forward and backward directions)?
Correct Answer :
More than three
Solution :
The correct option is More than three.
To find the pairs of digits in the given number 48261539 that have the same number of digits between them as in the standard numerical sequence, we need to check the distance between every pair of digits in both forward and backward directions.
A pair of digits satisfies this condition if the absolute difference between their positions in the number equals the absolute difference between their numerical values.
Let us list the digits along with their respective positions from left to right:
Position 1: 4
Position 2: 8
Position 3: 2
Position 4: 6
Position 5: 1
Position 6: 5
Position 7: 3
Position 8: 9
Now, let us evaluate the valid pairs step-by-step:
1. Pair (4, 2):
Digit 4 is at position 1 and digit 2 is at position 3.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (4, 2) is a valid pair.
2. Pair (8, 6):
Digit 8 is at position 2 and digit 6 is at position 4.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (8, 6) is a valid pair.
3. Pair (8, 3):
Digit 8 is at position 2 and digit 3 is at position 7.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (8, 3) is a valid pair.
4. Pair (2, 5):
Digit 2 is at position 3 and digit 5 is at position 6.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (2, 5) is a valid pair.
5. Pair (6, 3):
Digit 6 is at position 4 and digit 3 is at position 7.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (6, 3) is a valid pair.
6. Pair (1, 3):
Digit 1 is at position 5 and digit 3 is at position 7.
Difference in positions =
Difference in values =
Since the position difference equals the numerical value difference, (1, 3) is a valid pair.
Thus, there are a total of 6 such pairs, which is More than three.
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