The following comes from Shakuntala Devi's book

*"Figuring - The Joy of Numbers"* page 123 :

Multiplying the number 12345679 by the __multiples of 9__,

gives a curious set of palindromic patterns :

12345679 x 9 = **111111111**

12345679 x 18 = **222222222**

12345679 x 27 = **333333333**

and so on.

Multiplying by **999999999** itself gives a number which is a mirror image of itself

12345679 x **999999999** = **12345678987654321**

incidentally, this product is a perfect square [ It's also Palindromic Square nr. **91** ]

**111111111 **^{2} = **12345678987654321**

Many people find the above square quite useless but nevertheless fascinating !