What digits can you choose so that you get a 1-digit number in the first step itself? Give some examples. Describe the pattern in the digits.
To get a 1-digit number in the first step, choose consecutive digits (digits that differ by 1).
Examples:
- (4,5): 54 - 45 = 9
- (3,4): 43 - 34 = 9
- (7,8): 87 - 78 = 9
- (1,2): 21 - 12 = 9
Pattern: When two digits differ by 1, the difference between the two-digit number and its reverse is exactly 9, which is a 1-digit number.
Explanation
When digits differ by 1, the difference 9(a-b) = 9(1) = 9, which is already a single digit. This is shown in Mira's table where digits 4 and 5 give difference 9 in one step.
Solution Steps
Step 1: For 1-digit result in first step, need difference = 9
Step 2: Since difference = 9 × (difference of digits), we need difference of digits = 1
Step 3: Consecutive digits like (4,5), (3,4), (7,8) work