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Logic Puzzle # 116 Logic Problems Help



Logic Problem Solution:
Rookie Cards

By clue 1, Bo bought a 1986 Barry Bonds rookie card. Since by the introduction no two cards cost the same amount, and since Greg's purchase cost half as much as Bo's (1), Greg didn't buy the 1987 Greg Maddux, which cost half as much as Jeff's new card (3), or the 1990 Sammy Sosa, which cost half what Warren's rookie card did (5). Since Greg spent less than Bo (1), by clue 4, Greg also didn't buy the two Hall-of-Famers' cards, the 1957 Al Kaline and the 1957 Jim Bunning. Greg bought the 1987 Mark McGwire rookie card--for $6.00 (6). Then Bo spent $12.00 (1), the 1957 Jim Bunning cost $16.00, and the 1957 Al Kaline went for $20.00 (4). Neither the 1987 Greg Maddux (3) nor the 1990 Sammy Sosa (5) rookie card cost the most, so the 1957 Al Kaline at $20.00 was the most expensive of the six cards. Neither Chad nor Ian bought the 1957 Al Kaline for the highest amount (2), so either Jeff or Warren did. Then by clues 3 and 5, the fifth card to the four already named sold for $10.00 and is either the 1987 Greg Maddux (3) or the 1990 Sammy Sosa (5). The sixth card is the other of the Maddux and Sosa and had to sell for less than $10.00, since it was half the cost of one of the four cards other than the Kaline already named. Neither Jeff (3) nor Warren (5) could have bought the sixth card for under $10.00, or there then would be a seventh purchase. If Chad had bought the sixth card for under $10.00, there would be no card under Chad's for Ian to have bought. Ian bought the sixth card, by clue 7 the 1990 Sammy Sosa. The rookie card that went for $10.00 was the 1987 Greg Maddux. Jeff then spent $20.00 on the Al Kaline rookie card (3). If Warren had purchased the Greg Maddux card, by clue 5, Ian would have spent $5.00 on the Sammy Sosa. By elimination, then, Chad would have paid $16.00 for the Jim Bunning card, $11.00 more than Ian spent and a conflict with clue 2. So, Warren bought the 1957 rookie card of Hall of Fame pitcher Jim Bunning for $16.00, and Ian paid $8.00 for the Sosa (5). Chad acquired Greg Maddux's rookie card for his collection. The six boys bought their rookie cards on eBay as follows:

  • Jeff, 1957 Al Kaline, $20.00
  • Warren, 1957 Jim Bunning, $16.00
  • Bo, 1986 Barry Bonds, $12.00
  • Chad, 1987 Greg Maddux, $10.00
  • Ian, 1990 Sammy Sosa, $8.00
  • Greg, 1987 Mark McGwire, $6.00



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