THIRD ANSWERS 39 X 402 • 15678 27 X 594 = 16038 54 X 297 = 16038 36 X 495 = 17820 45 X 396 = 17820 52 X 367 = 19084 78 X 345 = 26910 46 X 715 = 32890 63 X 927 = 58401 Clement Wood, on page 48 of A Book o f M athematical Oddities (Little Blue Book No. 1210), published in Girard, Kansas, by Haldeman-Julius, undated), points out that 27 x 594 = 16038 is unique in that one factor is a multiple of the other (594 = 27 x 22). Incidentally, the Little Blue Books was an innovative and provocative series. The books were published by an American socialist and freethinker, Emmanuel HaldemanJulius, and were forerunners of today’s paperbacks. The books measured 3V2 by 5 inches, and sold by the hundreds of millions during the twenties and thirties for five cents each. There were thousands of titles. The seven solutions for the nine positive digits are given on page 65 of Albert Beiler’s Recreations in the Theory o f Numbers. He adds the following equalities: 4 X 1738 = 6952 4 X 1963 = 7852 3 X 51249876 = 153749628 6 X 32547891 = 195287346 9 x 16583742 = 149253678 Is it possible to group the nine positive digits into three triplets that have a product containing the same nine digits? Yes, though I do not know the total number of solutions. Hilario Fernandez Long, of Argentina, worked by hand on this problem in 1972. The highest product he found is 435918672, which equals 567 x 843 x 912. The lowest product he found is 127386945 = 163 x 827 x 945. His
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