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 Category: Logic Submitted By: eighsse Fun: (2.3) Difficulty: (2.85)

The Detroit Tigers played the Cincinnati Reds in the World Series (Major League Baseball). In this particular series (which went the full seven games), there was only one shutout, and no team scored more than 12 runs in any game. Following are some facts that apply to BOTH teams, individually, pertaining to the number of runs scored in each of the 7 games (no information is given about the order in which these games occured). For each team, there were:

[1] 4 games with a prime number of runs.
[2] A multiple of 3 games with an even number of runs.
[3] No two games, the product of whose runs was a prime number.
[4] 2 games with a perfect square of runs.
[5] No game with exactly 5 runs.

The Tigers scored 30 runs in the entire series, and [6] scored 7 or 8 runs in at least one game. The Reds scored 36 runs, and [7] of all seven games, there are exactly two pairs of games, the sum of whose runs was exactly 9 (a game can be used in multiple pairs).

Based on this information, which of these statements is accurate?
1. The Detroit Tigers won the World Series.
2. The Cincinnati Reds won the World Series.
3. The World Series winner is uncertain.

The bracketed clue numbers [1]-[7] are used for reference in the answer explanation.

 Posted by charlottes-odd 12/17/13 A series of headaches... That's what I keep getting! (literally, I'm not too well at the moment) good teaser eighsse :) Posted by eighsse 12/17/13 I'm sorry :( Feel better Posted by dewtell 01/03/15 Nice one. I got stuck by convincing myself early on that the two pairs of games that added to 9 could not consist of four separate games (somehow I overlooked the 3-3-12 extension), so I convinced myself there was no solution. Posted by eighsse 01/03/15 Glad you enjoyed it, and it's great that you were even able to approach the problem at all, let alone get that far. :)

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