Where do the numbers come from? In "The number devil" Hans Magnus Enzenberger tells us how we can create the numbers 2,3,4,5,6,7, 8 and 9 almost out of nothing. All that is needed is the number 1. See it for yourself. Just multiply 11 * 11 and you get 121. Magically the 2 has appeared. Now multiply 111*111 and you get 12321. Now you got the 3 out of nowhere. Next try 1111*1111. Do you already see a pattern? Yes, the right answer is 1234321. 11111*11111 equals, I think you can guess it now, 123454321. 111111*111111=12345654321 and 1111111*1111111 = 1234567654321 and 11111111*11111111=123456787654321 and finally 111111111*111111111=12345678987654321. Cool, eh?!
Welcome to the fantastic world of numbers!
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
If you multiply even bigger numbers all composed of 1s the pattern breaks down however as 1111111111*1111111111=1234567900987654321 and 11111111111*11111111111= 123456790120987654321 etc.
You can kind of understand this if you try to multiply these numbers by long multiplication e.g.:
11111 * 11111 =
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
+
1
1
1
1
1
0
0
0
0
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
4
3
2
1
If you multiply with more than 9 1s then you get carry overs and therefore the magic breaks down.
references
The number devil by Hans Magnus Enzenberger, ISBN-13: 978-0805062991
