Nine Ones Squared Make a Perfect Palindrome

111,111,111 times 111,111,111 equals 12,345,678,987,654,321.

Write out the long multiplication and each column simply counts how many ones land in it: one, two, three, up to nine and back down, with nothing to carry. The same pattern works for shorter strings, such as 111 times 111, which is 12,321.

Check it yourself

You can do this one on a calculator that handles 17 digits, or by long multiplication if you have an afternoon free. We checked it with a short computer program.