In this cryptarithm, each letter above the line represents a digit differing by 1 from the digit represented by the same letter below the line. For example, if A=3 above the line, then A=2 or A=4 below the line. All occurrences of a letter on the same side of a line represent the same digit. It is also known that there are total of five digits in the solution.

 ADABA
+CACBA
------
 DBABC

Actually 8 + 8 = 7 works for B+B=B and so does 1 + 1 = 2.

Using mimimal trial and error, we can see the left column is where we should begin. It can't carry, so unless A is 0 which can't happen (since ADABA begins with A) A+C=A can't carry either. So top C must equal 1 since the top A must be less than the bottom A.

We know A + A = C. So bottom C is 0 or 2. If bottom C is 2, top D has to be 5 and bottom D has to be 8, which doesn't work. So bottom C must be 0 and since top A isn't 0, top A must be 5 and carry, which results in bottom A being 6. 0 + 0 = 1 is the only B value that is carried into and doesn't carry out, so 0 must be top B and 1 must be bottom B. By doing addition to figure out what top D and bottom D are, we can figure out what the final equation is, which is 56505 + 15105 = 71610.

Posted by Gamer on 2004-08-11 14:47:05