## A Series of Headaches

Logic puzzles require you to think. You will have to be logical in your reasoning.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.

[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.

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