Try the puzzle using any other pair of digits. What is common to these differences? What do you get in the end?
Using any pair of digits: All differences are multiples of 9, and the process always ends with 9.
Example 1: Digits 1 and 9: 91 - 19 = 72 72 - 27 = 45 54 - 45 = 9
Example 2: Digits 2 and 8: 82 - 28 = 54 54 - 45 = 9
Common Property: All intermediate differences are multiples of 9, and the final result is always 9.
Explanation
The chapter shows through Mira's table that the difference between numbers formed by two digits is always 9 times the difference between the digits. This property ensures that all differences in the process are multiples of 9, eventually converging to 9.
Solution Steps
Step 1: Try digits 1 and 9: 91 - 19 = 72, 72 - 27 = 45, 54 - 45 = 9
Step 2: Try digits 2 and 8: 82 - 28 = 54, 54 - 45 = 9
Step 3: All differences are multiples of 9, ending at 9