Writing the problem as
A = n*B for n=1,....,9
it is easy to see that B must have four digits and A five. Now we check every combination of A in [1000,9999] and n in [1,9] andf look for combinations that have each of the digits 1,...,9 exactly once. This can be done by a computer program (and in fact Carlos and I independently wrote a version - one in Ubasic, one in FORTRAN77) to come up with the following table:
1/2: 6729 13458 6792 13584 6927 13854 7269 14538 7293 14586 7329 14658 7692 15384 7923 15846 7932 15864 9267 18534 9273 18546 9327 18654 1/3 5823 17469 5832 17496 1/4 3942 15768 4392 17568 5796 23184 7956 31824 1/5 2697 13485 2769 13845 2937 14685 2967 14835 2973 14865 3297 16485 3729 18645 6297 31485 7629 38145 9237 46185 9627 48135 9723 48615 1/6 2943 17658 4653 27918 5697 34182 1/7 2394 16758 2637 18459 4527 31689 5274 36918 5418 37926 5976 41832 7614 53298 1/8 3187 25496 4589 36712 4591 36728 4689 37512 4691 37528 4769 38152 5237 41896 5371 42968 5789 46312 5791 46328 5839 46712 5892 47136 5916 47328 5921 47368 6479 51832 6741 53928 6789 54312 6791 54328 6839 54712 7123 56984 7312 58496 7364 58912 7416 59328 7421 59368 7894 63152 7941 63528 8174 65392 8179 65432 8394 67152 8419 67352 8439 67512 8932 71456 8942 71536 8953 71624 8954 71632 9156 73248 9158 73264 9182 73456 9316 74528 9321 74568 9352 74816 9416 75328 9421 75368 9523 76184 9531 76248 9541 76328 1/9 6381 57429 6471 58239 8361 75249
Source: Carlos Rivera (crivera@ux1.sci.net.mx)
Michael J. Winckler (Michael.Winckler@iwr.uni-heidelberg.de)
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