How many such pairs of digits are there in the number ‘40585636’, each of which has as many digits between them as they have in the number series (Only in backward direction)?
Correct Answer :
Two
Solution :
The correct answer is Two.
To find the pairs of digits in the number 40585636 that have as many digits between them as they have in the standard numerical series (only in the backward direction), we analyze the number from right to left (backward direction).
Let us write down the digits of the number along with their positions from left to right (1-based index):
Position 1: 4
Position 2: 0
Position 3: 5
Position 4: 8
Position 5: 5
Position 6: 6
Position 7: 3
Position 8: 6
Now, we look for pairs of digits counting in the backward direction (from right to left) where the difference in their positions matches the difference in their values in the standard number series (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Let's check each digit starting from the rightmost digit:
1. Starting from digit 6 (Position 8):
Counting backward (upwards from 6): 6 (Pos 8) → 7 (Pos 7) → 8 (Pos 6) → 9 (Pos 5). None of these match the actual digits at these positions (which are 3, 6, and 5 respectively).
2. Starting from digit 3 (Position 7):
Counting backward: 3 (Pos 7) → 4 (Pos 6) → 5 (Pos 5).
Here, the digit at Position 5 is 5, which matches our count.
Thus, the pair is (3, 5). In the standard number series, there is one digit (4) between 3 and 5, and in the given number, there is also one digit (6) between them.
3. Starting from digit 6 (Position 6):
Counting backward: 6 (Pos 6) → 7 (Pos 5) → 8 (Pos 4).
Here, the digit at Position 4 is 8, which matches our count.
Thus, the pair is (6, 8). In the standard number series, there is one digit (7) between 6 and 8, and in the given number, there is also one digit (5) between them.
4. Starting from digit 5 (Position 5):
Counting backward: 5 (Pos 5) → 6 (Pos 4) → 7 (Pos 3) → 8 (Pos 2) → 9 (Pos 1). None of these match the actual digits.
5. Checking other digits:
Continuing this process for the remaining digits (8, 5, 0, 4) yields no further matches in the backward direction.
Therefore, there are exactly two such pairs of digits: (3, 5) and (6, 8).
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