The magical number!

                                                              1089 -THE MAGIC NUMBER!

1089 is taken as magic number. In ancient time it was said that this special number can ward away evil spirits.

What is special about 1089 or what makes it magical? Let us consider 2 cases here:

1. 

i. Given a non-palindromic 3-digit number (i.e. a number in which the first and the last digit are not the same e.g. 389, 712, 658 etc.

ii. Let us pick 389 for example.

iii. Reverse the number i.e. we have now 983.

iv. Subtract the smaller from the bigger one, gives 594 (i.e. 983-389)

v. Add 594 to its reverse gives 1089 (594+495)

As many examples of this 3 digit non palindromic number you continue to get 1089

• Can you give the reason for this? Try to do so. The reason will come out in the next write up.

2. 

Another is the pattern been formed by multiplying the number by integers from 1 to 9:

Note the patterns within each column of the answer:

1 × 1089 = 1089

2 × 1089 = 2178

3 × 1089 = 3267

4 × 1089 = 4356

5 × 1089 = 5445

6 × 1089 = 6534

7 × 1089 = 7623

8 × 1089 = 8712

9 × 1089 = 9801

• Really amazing!