Problem : 2+2 = 22 Liberty : Solve by binary or other numbering system. Taking advantage of "any other numbering system" defined in the query,I proceed as There are numerous system except binary. we can as well define a system ... a coding system and can prove this. I have come across 2 ways of solving this problem. 1. 2 in binary = 00010 so 00010 + 00010 ---------------- 10110 ( which is 22) Considering a coding scheme in which 0 + 0 = 0 or 1 (which toggles each time) and 1 + 1 = 1 or 0 ( which toggles each time) 2. Anyone with some knowledge of binary system may well know Gray codes.( that goes like 0, 1 , 11 , 10 , 110. toggling) Lets define new gray code - name it kiwigray code.. where instead of starting from 0, 1 , 11, 10.. we start the code with 00000 as 0 00100 as 1 00110 as 2 00010 as 3.. proceding this way we can end up having 01100 as 22. thus 00100(2) + 00100 (2) = 01100 (22) QED :) cheers!