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.

(In reply to No Subject by Hannah Caldwell)

Hannah, 3 can't be the false one. That would mean the catcher has a batting average less than .300, and Henry has an average above .300, but Henry's average is lower than the catcher's.

Here's the solution:

1, 5, and 6 cannot all be true. If catcher < .300 and Henry > .300, then .300 < Henry < catcher < .300 is impossible. Therefore the lie is either 1, 5, or 6, and we know that 2, 3, and 4 are all true.

Also, 3, 5, and 6 cannot all be true. Clue 6 says that Henry has to be the centerfielder, who by clue 3 is known to bat .295. But clue 5 says that Henry bats over .300. Therefore the lie is either 3, 5, or 6, and we know that 1, 2, 4 are all true.

Putting that together, we know that 1, 2, 3, 4 are all true.

From clues 1 and 3 we know that the catcher bats less than .300 but not .295 because that is the centerfielder. Therefore the catcher bats .280.

Notice clue 6 now. Clue 6 said that someone (Henry, but that doesn't matter) bats lower than the catcher. But NONE of the averages are lower than the catcher's 0.280. Therefore we know that 6 is the lie and 5 is true.

Moving on…

From clues 1 and 4 we know Ken and Leo both score less than .300. We already determined that the catcher and the centerfielder have the two scores that are less than .300. Therefore Ken and Leo are the catcher and centerfielder.  However, from clue 1, we know that Leo and the catcher cannot be the same person.

Therefore we have Ken is the catcher with .280 and Leo is the centerfielder with .295.

From clues 2 and 4 we know (1) Ken, (2) Clements, (3) the rightfielder, and (4) the .395 guy are all different people.

Leo the centerfielder with .295 can't be person (3) because we already know that person is the rightfielder. He also can't be person (4) because that person bats .395.  And of course he can't be person (1) because that is Ken =)

Therefore Leo must be person (2) and we have Leo Clements the centerfielder with .295.

By the way, by elimination, we know that person (4) is the leftfielder and that person (3) bats .310.

From clue 5 we know that Brooks scored over 0.300 (so he is either Stan or Henry) but he isn't Henry, so he must be Stan.

From clue 4 we know that Stan scored 30 points higher than Ken, who bats .280, so Stan bats .310.  So Stan Brooks is person (3) and we have the solution:

1) Ken Ashley, C, .280
2) Leo Clements, CF, .295
3) Stan Brooks, RF, .310
4) Henry Dodson, LF, .395

I thought i only had half as solution (as my subject notes) but I figured it out.  Hence the edit.

Edited on April 15, 2005, 7:56 pm

Posted by nikki on 2005-04-15 19:46:06