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A remarkable multiplication (Posted on 2008-11-09) Difficulty: 3 of 5
In the multiplication below, each digit from 0-9 appears exactly 2 times. Decode the multiplication.
       * * *
       * * *
     -------
       * * *
     * * *
   * * *
   ---------
   * * * * *
Note1: No leading zeros in any number.
Note2: For a long time, mathematicians thought that this problem could only be solved using a computer. A few years ago, it was solved analytically, but its solution itīs far from being simple (and short). So, welcome computers.

See The Solution Submitted by pcbouhid    
Rating: 5.0000 (1 votes)

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Computer Solution Comment 3 of 3 |

Two loops (100..999); test product > 9999 and < 99999; three multiplications tested each > 99 and < 999; count occurrences of the ten digits (two of each),  -- under 0.1 seconds.  Sole solution:

179 * 224 = 40096 (lines 716, 358, 358)

The only remarkable property seems to be that this is a unique solution.  I'll look at the previous posts to see if anyone found a solution by heuristics.


  Posted by ed bottemiller on 2008-11-10 22:14:44
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