In the multiplication below, each digit from 0-9 appears exactly 2 times. Decode the multiplication.
* * *
* * *
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* * *
* * *
* * *
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* * * * *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.
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.
Computer Solution
