Logic Puzzle # 69 Logic Problems Help

Logic Problem Solution:

From the introduction, the new Ridge Road goes from Summerset south to Winterhaven a distance of 50 miles. By clue 10, the first exit out of Summerset is 10 miles, so the distance sign there is 40 miles to Winterhaven; and the last exit before Winterhaven is 5 miles north of the city. By clue 1, the exit for Longview is 20 miles farther from Winterhaven than the exit where there is food; while by clue 4, the exit for Rte. 770 is 20 miles farther from Winterhaven than the Dante's Choice exit. Since Rte. 770 isn't the Longview road (12), there isn't complete overlap between the clues. Further, the clues can't intersect with the exit at Rte. 770 being for food, or, given that the first exit south on Ridge Road is 40 miles from Winterhaven, Dante's Choice would be 0 miles from Winterhaven. So, between clues 1 and 4, four different exits are named. By clue 7, the Cozy Valley exit is 20 miles farther from Winterhaven than the exit onto Rte. 56. Cozy Valley can't be the exit for food, or the Rte. 56 exit would be 0 miles from Winterhaven (1, 7); and Rte. 56 can't be the Longview road, or the exit where food is available would be 0 miles from Winterhaven (1, 7). So, there is no overlap between clues 1 and 7. Since Rte. 56 doesn't go to Dante's Choice (13), there is also no overlap between clues 4 and 7. Therefore, all six exits are named among clues 1, 4, and 7: Longview 20 miles farther than the food available exit, Rte. 770 20 miles farther than Dante's Choice, and Cozy Valley 20 miles farther than the exit onto Rte. 56. By clue 2, the exit for Wild Lake is twice as far from Winterhaven as the exit where the state park is located. Since the Wild Lake exit isn't onto Rte. 770 (12), the Wild Lake exit is either onto Rte. 56 or for food. If the Wild lake entrance were the Rte. 56 one, given that Cozy Valley were the first exit, the Wild Lake exit would at most be 20 miles from Winterhaven (7) and the state park then at most 10, so the state park couldn't be at the Longview (1) or Rte. 770 (4) exit. The state park exit would be at Dante's Choice--no (8). So, the Wild Lake exit is the one where food is available. Given that Longview were the first exit, Wild Lake would be at most 20 miles from Winterhaven and the state park at most 10 (2); then neither the Rte. 770 (4) nor Cozy Valley (7) exit could be for the state park. The state park sign isn't at the Dante's Choice exit either (8). The state park is on Rte. 56. By clues 1, 2, and 7, the Longview exit must be farther from Winterhaven than Cozy Valley, so either the Longview or Rte. 770 exit is the first one, 40 miles from Winterhaven. If the Rte. 770 exit were 40 miles and Dante's Choice thus 20 (4), the state park would have to be the closest exit to Winterhaven (1,2,7), 5 miles north (10), with Cozy Valley 25 away (7), Wild Lake 10 away (2), and Longview 30 away (1). However, the data in clue 5, that the exit for fuel is 5 miles farther from Winterhaven than the High Tor exit, cannot work with this mileage arrangement. Therefore, the Longview exit is the first exit, 40 miles north of Winterhaven. The Wild Lake/food exit is 20 miles (1), Rte. 56/state park exit 10 miles (2), and Cozy Valley exit 30 miles (7) from Winterhaven. The Dante's Choice exit must then be the closest one, 5 miles north, with the Rte. 770 exit 25 miles away (4). By clue 5, the exit for fuel must be at Cozy Valley, and High Tor is on Rte. 770. By elimination, the state park is at the Spring Hollow exit. By clue 9, the Rte. 29 exit is 5 miles farther from Winterhaven than the exit for camping; so Rte. 29 must be the Cozy Valley exit, and camping is available at the Rte. 770/High Tor exit. The exit for the scenic view is the Dante's Choice exit (6), with lodging at the Longview exit. The latter exit isn't Rte. 88 (3) or Rte. 213 (11) and is Rte. 197. Rte. 213 goes to Dante's Choice and Rte. 88 to Wild Lake (11). The Ridge Road signs, with distances south to Winterhaven, are placed as follows:

• Exit 1S -- 40 mi., Rte. 197, Longview, lodging
• Exit 2S -- 30 mi., Rte. 29, Cozy Valley, fuel
• Exit 3S -- 25 mi., Rte. 770, High Tor, camping
• Exit 4S -- 20 mi., Rte. 88, Wild Lake, food
• Exit 5S -- 10 mi., Rte. 56, Spring Hollow, state park
• Exit 6S -- 5 mi., Rte. 213, Dante's Choice, scenic view