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.
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