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Cycling for a Cure
 Seven cyclists ride a 300-mile relay from Summerset to Ocean City.
 April 19, 2004
 From the introduction, a different cyclist rode each of the seven legs, which begin and end in cities along the 300-mile route starting in Summerset and ending in Ocean City. Between clues 5 and 8, either all six legs in addition to the 20-mile long shortest one (clue 1) are described; or there is some overlap between the clues. If Rob in clue 8 had ridden the Glen Falls-to-Central City leg in clue 5, given that the 1st leg was more than 20 miles (8, 1) and that no legs are the same mileage (1), Rob would have cycled more than 50 miles (8) and Tom then more than 75 miles (5)--no (1). If Mr. Price in clue 8 were Tom in clue 5, with Ms. Dunn's leg then more than 20 miles (5, 1), Tom Price's leg would have been more than 65 miles (5) and Rob's then more than 85 (8)--again contradicting clue 1. Since Mr. Price's leg ended in Bayview (2), he didn't ride the leg from Glen Falls to Central City. If the cyclist who rode the 1st leg in clue 8 were Tom in clue 5, with Ms. Dunn's leg then more than 20 miles (5, 1), Rob's journey would have covered more than 95 miles (5, 8)--again, no (1). Since the 1st leg started in Summerset, it couldn't have begun in Glen Falls; and since Ms. Dunn started riding in Mt. Holly (13), she didn't ride the 1st leg. Therefore, all seven legs are given between clues 5 and 8: Tom's, the one from Glen Falls to Central City, Ms. Dunn's, Rob's, Mr. Price's, the 1st leg, and the shortest leg of 20 miles. Either Tom or Rob rode the 75-mile longest (1) relay. If Rob had ridden the 75 miles, Mr. Price would have cycled 55 miles and the 1st leg would have been 45 miles long. Summing these legs with the 20-mile one, we get 195 miles, leaving 105 miles for the three cyclists in clue 5. Letting Ms. Dunn's leg equal X, the Glen Falls-to-Central City leg would be X + 25 miles and Tom would have ridden X + 50 miles--a total of 3X + 75 = 105 or X = 10. But Ms. Dunn can't have pedaled only 10 miles (1). Therefore, Tom rode the 75-mile leg, ending in Glen Falls (11), with the distance from Glen Falls to Central City then 50 miles and Ms. Dunn's route covering 25 miles (5). Summing with the 20-mile leg, we get 170, leaving 130 miles for the three in clue 8. Letting the distance of the 1st leg equal X, Mr. Price cycled X + 10 and Rob X + 30 miles, so that 3X + 40 = 130, or X = 30. The 1st leg, going from Summerset to the next city, is 30 miles long, Mr. Price cycled 40 miles, and Rob rode 60 miles. By clue 6, cyclist Koontz rode 15 miles farther than the one who rode the last leg into Ocean City. Koontz must be Tom, with the 7th leg then the 60-mile-long one. The city at the end of the 1st leg isn't Fort Hill (3). By clue 10, then, Fort Hill can't be the start of the last leg and must be the 40-mile-long relay that Price pedaled, with Fort Hill the terminus of the shortest leg. By clue 14, Ms. Close cycled 50 miles and Faith Dunn 25. By clue 4, Wes rode 10 miles longer than Jeff. If Wes had ridden the 30 miles and Jeff the 20, one of the three women would have to be Mr. Price. So, Wes is Price, and Jeff rode the 1st leg of 30 miles. Beth is Ms. Close (12), and Sue rode the 20-mile leg. Sue is Ives (7). By clue 9, Jeff is Moore and Rob Young. Getting the legs solved, then, Mr. Price finished his leg in Bayview (2); and Ms. Dunn started riding in Mt. Holly (13). The 1st leg had to end in Mt. Holly, and the leg beginning in Mt. Holly ended in Autumndale. By clue 15, Rob didn't start his ride in Central City; so the leg ending in Fort Hill started in Central City. Since we have legs going from Summerset to Mt. Holly and Mt. Holly to Autumndale, the leg starting in Autumndale can't end in Ocean City and thus ends in Glen Falls. The final leg starts in Bayview. In sum, the seven Cycled for a Cure as follows: Summerset to Mt Holly, 30 miles, Jeff Moore Mt. Holly to Autumndale, 25 miles, Faith Dunn Autumndale to Glen Falls, 75 miles, Tom Koontz Glen Falls to Central City, 50 miles, Beth Close Central City to Fort Hill, 20 miles, Sue Ives Fort Hill to Bayview, 40 miles, Wes Price Bayview to Ocean City, 60 miles, Rob Young