This quite amazing triangular palindrome, (a number that reads the same way backwards as forwards), can be developed entirely by the various products formed using only one digit: the number one.

We start off with the simplest possible product:

1 x 1 = 1

Any single digit is a trivial palindrome, so this product produces a palindrome.

Let’s extend to double digits of the number one.

11 x 11 = 121

This product is also a palindrome. Is there a pattern forming here?

Can you guess the product of triple digits of the number one?

111 x 111 =?

Click to see solution..


111 x 111 = 12321

We can represent the answers established so far in a triangular pattern.

1 x 1       =       1

11 x 11     =     121

111 x 111   =   12321

Complete six more iterations.