Solution to: Fabulous Fraction
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.
Back to the puzzle