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 The Midville Muddlers (Posted on 2005-04-15)
In this problem the puzzles each contain a series of statements. However you will find (or will have to find) that one statement is false. It will be necessary for you to find the false one in order to solve the puzzle.

The Midville Muddlers baseball team depends on four players to score most of their runs. The positions of the four are the three outfielders (rightfielder, centerfielder, and leftfielder) and the catcher. From the statements that follow, determine the first name (Henry, Ken, Leo, or Stan), surname (Dodson, Brooks, Clements, or Ashley), position, and batting average of each player. (The averages: .280, .295, .310, .325)

1. Neither Leo nor the catcher has a batting average over .300.

2. Three who are neighbors are Clements, the rightfielder, and the player who bats .325.

3. The centerfielder bats .295.

4. Stan's batting average is 30 points higher than that of Ken, who does not live near any of the other three.

5. Brooks and Henry, who is not Ashley, both bat over .300 and are in competition to see which will score the most runs this season.

6. Henry, who is neither the rightfielder nor the leftfielder, has a lower batting average than the catcher.

Remember one of these is false.

 No Solution Yet Submitted by ron Rating: 3.5556 (9 votes)

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 sol'n | Comment 21 of 22 |

The false statement is (6):

Assume (6) holds, this means Henry is CF, and has a lower avg than the catcher.  If (5) also holds, Henry bats .310, and Brooks is catcher and bats .325.  This contradicts both (3) and (1), so (5) and (6) can't both hold.  Suppose (5) doesn't hold but (6) does.  By (3), Henry bats .295, but this contradicts (1).  Therefore, (6) must not hold.

Thus, the lineup is as follows:

• RF Stan Brooks .310
• CF Leo Clements .295
• RF Henry Dobson .325
• C Ken Ashley .280

 Posted by josh on 2005-06-28 20:14:56

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