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Logic Puzzle # 154 Logic Problems Help



Logic Problem Solution:
The Good Sport

From the introduction, no two donations Buzz made to sports teams were for the same amount of money, and the six donations totaled $1500. By clue 1, Buzz gave the basketball team twice as much as the Knights, to whom he gave $50 more than to the Devils (clue 8); and by clue 6, Buzz gave the Hawks twice as much as the soccer team, to which he donated $50 more than to the Rovers (3). Between the two clues, then, either all six teams are named or there is some commonality. If all six donations are listed, then either the Devils (1, 8) or the Rovers (6, 3) would have gotten the least, $50 (5). If the Devils had received the $50, by clues 8 and 1, the Knights would have received $100 and the basketball team $200. Then the three teams in clues 3 and 6 would have received $1500-$350, or $1150. Adding the amounts in the two clues with the Rovers getting X, the soccer club would have gotten X+$50 and the Hawks 2X+$100, a total of 4X+$150. So, solving, 4X+$150 = $1150, or X would equal $250. But the Hawks then would have received $600 from Buzz, contradicting clue 7. If the Rovers had received the $50 from Buzz, then the Devils would have had to get more than $50 and the basketball team would have received the largest donation--no (9). Therefore, there must be some overlap between the two sets of teams in clues 1, 8 and 6, 3. The Hawks aren't the basketball team and the Knights aren't the soccer team, since then the Devils and Rovers would have received the same sum, contrary to the introduction. If the Devils were the soccer team, then combining the four clues, given that the basketball team didn't get the biggest amount (9) and that the Rovers therefore got the least, $50, the Devils would have received $100, the Knights $150, the Hawks $200, and the basketball team $300, a total of $800. But the sixth team would have received $700, contradicting clue 7. So, the Rovers must be the basketball team. If the Devils weren't the $50 donees, then the five teams amomng the four clues would have received $1450 as follows: the Devils X, the Knights X+$50, the basketball Rovers 2X+$100, the soccer team 2X+$150, and the Hawks 4X+$300. Solving, 10X+$600 = $1450, or X = $85. But the Hawks then would have gotten $640--no (7). So, combining the clues, Buzz gave the Devils $50, the Knights $100, the basketball Rovers $200, the soccer squad $250, and the Hawks $500, a total of $1100, with the sixth team then getting $400. By clue 4, the soccer team is the Lions, and the Knights play baseball. By elimination, the sixth team that got $400 is the Comets. By clue 7, the Devils play hockey. The Hawks play football and the Comets softball (2). In sum, Buzz's deductible sports contributions in 2001 were as follows:

  • $500 to the Hawks football team
  • $400 to the Comets softball team
  • $250 to the Lions soccer team
  • $200 to the Rovers basketball team
  • $100 to the Knights baseball team
  • $50 to the Devils hockey team



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