Solution #30: A Story of 1's and 2's

 11...1  -  22...2 =  11...1 11...1  - 2(11...1)
 ------     ------    ------ ------      ------
2n times   n times   n times n times    n times

                   =  11...1 00...0  -   11...1
                      ------ ------      ------
                     n times n times    n times

                   =  11...1 x (100...0 - 1)
                      ------     ------
                     n times    n times

                   =  11...1 x 99...9
                      ------   ------
                     n times   n times

                   =  11...1 x 9 x 11...1
                      ------       ------
                     n times       n times

                   =  32   x 11...12
                             ------
                            n times

                   =         33...32
                             ------
                            n times

Example: 11 - 2 = 9 = 32.
Source: Berrondom, Marie
Categories: Reasoning, Number sense, Arithmetic, Magic
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