## Product Pairs

Use the digits 1-9 once each to create two multiplication problems, each with the same solution.  That is, (AxB) = (CxD), and all nine digits are used once to make the numbers (9 digits total in A, B, C, and D.)  How many such pairs of problems are there?

Source: Based on a Martin Gardner puzzle.

Solutions were received from Larry Corrado, Al Zimmermann, Denis Borris, Philippe Fondanaiche, galois722, Sumita Das, Claudio Baiocchi, and Kirk Bresniker.  Several people found all 59 solutions.  This is Sumita Das' summary:
```Assuming that A > B, C > D and A > C, we get 59 solution pairs to the problem A x B = C x D.
They are listed below:
134 x 29 = 67 x 58
138 x 27 = 69 x 54
146 x 29 = 73 x 58
158 x 23 = 79 x 46
158 x 32 = 79 x 64
174 x 23 = 69 x 58
174 x 32 = 96 x 58
186 x 27 = 93 x 54
259 x 18 = 74 x 63
459 x 8 = 136 x 27
476 x 9 = 153 x 28
532 x 14 = 98 x 76
534 x 9 = 267 x 18
538 x 7 = 269 x 14
546 x 9 = 273 x 18
584 x 12 = 96 x 73
586 x 7 = 293 x 14
638 x 7 = 154 x 29
654 x 9 = 327 x 18
658 x 7 = 329 x 14
759 x 8 = 132 x 46
782 x 9 = 153 x 46
897 x 4 = 156 x 23
984 x 7 = 123 x 56
1358 x 2 = 679 x 4
1372 x 4 = 98 x 56
1458 x 3 = 729 x 6
1538 x 2 = 769 x 4
1576 x 2 = 394 x 8
1584 x 3 = 792 x 6
1586 x 2 = 793 x 4
1728 x 3 = 96 x 54
1746 x 3 = 582 x 9
1749 x 2 = 583 x 6
1756 x 2 = 439 x 8
1824 x 3 = 96 x 57
1854 x 3 = 927 x 6
1869 x 2 = 534 x 7
1943 x 2 = 67 x 58
3451 x 2 = 986 x 7
3458 x 2 = 91 x 76
3672 x 1 = 459 x 8
3752 x 1 = 469 x 8
4296 x 1 = 537 x 8
4632 x 1 = 579 x 8
4736 x 1 = 592 x 8
4876 x 1 = 92 x 53
5392 x 1 = 674 x 8
5394 x 1 = 87 x 62
5432 x 1 = 679 x 8
5742 x 1 = 638 x 9
5823 x 1 = 647 x 9
5936 x 1 = 742 x 8
6352 x 1 = 794 x 8
7456 x 1 = 932 x 8
7524 x 1 = 836 x 9
7536 x 1 = 942 x 8
7624 x 1 = 953 x 8
7632 x 1 = 954 x 8
```

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