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Saturday, July 26, 2008

Fabulous Fraction

With all the numbers 0 up to 9 (using each number exactly once) you can make two fractions that add up to exactly 1.

The Question: How shall this be done?

Answer: There are 97 solutions to this problem, some of which can easily be calculated on the back of an envelope (such as 1/2+3548/7096), and others which are less trivial (such as 34/578+96/102).

Here, all possible solutions are shown:
1/2+3485/6970, 1/2+3548/7096, 1/2+3845/7690, 1/2+4538/9076, 1/2+4685/9370, 1/2+4835/9670, 1/2+4853/9706, 1/2+4865/9730, 1/4+7365/9820, 1/6+7835/9402, 1/7+4362/5089, 2/4+3079/6158, 2/6+3190/4785, 2/7+5940/8316, 2/7+6810/9534, 2/9+5803/7461, 3/6+1485/2970, 3/6+2079/4158, 3/6+2709/5418, 3/6+2907/5814, 3/6+4851/9702, 3/127+496/508, 4/5+1278/6390, 4/5+1872/9360, 4/356+792/801, 5/104+693/728, 6/324+795/810, 6/534+792/801, 7/9+1208/5436, 7/9+1352/6084, 7/54+893/1026, 8/10+729/3645, 8/10+927/4635, 8/512+693/704, 9/12+876/3504, 9/351+684/702, 10/28+369/574, 10/45+287/369, 10/45+728/936, 10/96+473/528, 12/54+609/783, 12/60+748/935, 12/96+357/408, 12/96+735/840, 13/26+485/970, 13/52+678/904, 15/30+486/972, 16/32+485/970, 17/89+504/623, 18/90+276/345, 18/90+372/465, 19/57+308/462, 19/58+273/406, 21/96+375/480, 24/63+507/819, 24/96+531/708, 27/54+309/618, 27/81+306/459, 27/81+630/945, 29/58+307/614, 29/87+310/465, 31/62+485/970, 32/48+169/507, 32/80+417/695, 34/51+269/807, 34/578+96/102, 35/70+148/296, 35/70+481/962, 36/81+405/729, 36/81+540/972, 38/61+207/549, 38/76+145/290, 38/76+451/902, 38/95+426/710, 39/51+204/867, 39/65+284/710, 42/87+315/609, 45/61+208/793, 45/90+138/276, 45/90+186/372, 45/90+381/762, 46/92+185/370, 48/96+135/270, 48/96+351/702, 54/87+231/609, 56/84+109/327, 56/84+307/921, 56/428+93/107, 56/832+97/104, 57/92+140/368, 57/204+98/136, 59/236+78/104, 60/1245+79/83, 63/728+95/104, 70/96+143/528, 74/89+105/623, 87/435+96/120.