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Logic Puzzle # 132 Logic Problems Help



Logic Problem Solution:
The Great Flying Contest

From the introduction, the summer science students divided into girl-boy pairs for the flying contest. By clue 5, the plane that landed in Four Corners went 3.0 mi. farther than Brent and his partner's design, which flew twice as far as Susan and her partner's plane. By clue 2, Alexis and her partner's creation landed 3.0 mi. farther from Summerset Tor than Daniel and his partner's. Daniel wasn't Susan's partner (9); so, Daniel and his partner are either the fourth pair to the three in clue 5 or Daniel and his partner's plane came down in Four Corners. By clue 1, the least distance any of the five planes flew was 3.0 miles. If Daniel and his partner's plane had come down in Four Corners, even letting Susan and her partner's distance be the least amount, by clues 5 and 2, Alexis and her partner's design would have flown 12.0 mi., conflicting with clue 1 which states that none of the planes flew farther than 10.0 mi. So, Daniel and his partner in clue 2 are the fourth pair to the three in clue 5. In clue 2, Alexis and her partner are either the fifth pair or had their plane land in Four Corners, or Alexis was Brent's partner. If Alexis and her partner's plane had landed in Four Corners, then both Daniel and his partner (2) and Brent and his partner (5) would have had their creations land 3.0 mi. short of Alexis and her partner's design, contradicting the introduction which says that no two planes went the same distance from Summerset Tor. Trying Alexis as Brent's partner, if Susan and her partner had had the plane that flew 3.0 mi. (1), by clues 5 and 2, Daniel and his partner's plane would have gone the same distance, contradicting the introduction. Similarly, if Daniel and his partner's design had gone the 3.0 mi., by clues 2 and 5, Susan and her partner's plane also would have flown 3.0 mi. So, if Alexis and Brent were partners, the fifth pair's plane would have gone the 3.0 mi. Then by clue 1, the planes of the four contestants already derived would have gone a total of 27.0 mi. Letting Susan and her partner's plane's flight equal X, Alexis and Brent's design would have flown 2X (5), the flight ending in Four Corners would have gone 2X+3.0 (5), and Daniel and his partner's aircraft would have covered 2X-3.0 (2) mi. Summing, 7X would equal 27.0, or X would equal 3.86 mi. However, the flight ending in Four Corners then would have gone 10.72 mi., contradicting clue 1. So, Alexis and Brent weren't partners; and Alexis and her partner in clue 2 are the fifth pair of competitors. By clues 2 and 5, either Daniel and his partner or Susan and hers had the plane that flew the 3.0 mi. (1). If Daniel and his partner's plane had gone that distance, Alexis and her partner's would have flown 6.0 mi. (2). Then the three flights in clue 5 would have totalled 21.0 mi. (1). Letting Susan and her partner's distance equal X, Brent and his partner's plane would have gone 2X and the plane landing in Four Corners would have covered 2X+3.0 mi. Summing, 5X+3.0 would equal 21.0, and X would equal 3.6. However, the plane setting down in Four Corners then would have traveled 10.2 mi., contradicting clue 1. Therefore, Susan and her partner's aircraft covered the low of 3.0 mi. (1), Brent and his partner's design went 6.0 mi., and the plane landing in Four Corners came down 9.0 mi. from Summerset Tor. By clue 1, then, Alexis and her partner's and Daniel and his partner's planes totalled 12.0 mi. Letting Daniel and his partner's distance be X, Alexis and her partner's creation would have gone X+3.0 mi. Solving, 2X+3.0 = 12.0, or X equals 4.5. Daniel and his partner's plane flew 4.5 mi. and Alexis and her partner's covered 7.5 mi. By clue 4, Daniel and his partner's aircraft reached Hollyville, and Tony was Susan's partner in the event. Alexis partnered with Jeff (2, 6), and Peter was part of the top flight team whose plane flew to Four Corners. By clue 3, Alexis and Jeff's aircraft got as far as Great Springs. Leah was Daniel's partner, and Susan and Tony's plane landed in Rancho Linda (7). By elimination, the plane that came down in Mt. Pisgah was built by Brent and his partner. She was Carrie, and Mia partnered with Peter (8). The five summer science class planes flew from Summerset Tor as follows:

  • Mia & Peter's, 9.0 mi. to Four Corners
  • Alexis & Jeff's, 7.5 mi. to Great Springs
  • Carrie & Brent's, 6.0 mi. to Mt. Pisgah
  • Leah & Daniel's, 4.5 mi. to Hollyville
  • Susan & Tony's, 3.0 mi. to Rancho Linda



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