Magic in mathematics I

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” 
-- Bertrand Russell

Most people know that 1 * 1 = 1, fewer have realized that 11 * 11 = 121. Nothing too special about that. But hey, try one more: 111 * 111 = 12321. 1-2-3-2-1 hmm.. interesting.. what about 111111111 * 111111111 Yes you gussed it! 12345678987654321. I leave you to fill out the gaps or even continuing adding extra numbers! With a bit of addition and multiplication you can create a lot of fun patterns. Here are my favorites. Can you find more patterns? If you do find anything of interest, email me so I can post it here.

        1 * 8 + 1 = 9

       12 * 8 + 2 = 98

      123 * 8 + 3 = 987

     1234 * 8 + 4 = 9876

    12345 * 8 + 5 = 98765

   123456 * 8 + 6 = 987654

  1234567 * 8 + 7 = 9876543

 12345678 * 8 + 8 = 98765432

123456789 * 8 + 9 = 987654321

Try using 9 instead of 8...

        1 * 9 + 2  = 11

       12 * 9 + 3  = 111

      123 * 9 + 4  = 1111

     1234 * 9 + 5  = 11111

    12345 * 9 + 6  = 111111

   123456 * 9 + 7  = 1111111

  1234567 * 9 + 8  = 11111111

 12345678 * 9 + 9  = 111111111

123456789 * 9 + 10 = 1111111111

And its reverse..

       9 * 9 + 7 = 88

      98 * 9 + 6 = 888

     987 * 9 + 5 = 8888

    9876 * 9 + 4 = 88888

   98765 * 9 + 3 = 888888

  987654 * 9 + 2 = 8888888

 9876543 * 9 + 1 = 88888888

98765432 * 9 + 0 = 888888888

finally,

        1 * 1         =         1

       11 * 11        =        121

      111 * 111       =       12321

     1111 * 1111      =      1234321

    11111 * 11111     =     123454321

   111111 * 111111    =    12345654321

  1111111 * 1111111   =   1234567654321

 11111111 * 11111111  =  123456787654321

111111111 * 111111111 = 12345678987654321

Have fun..