### Brain Teasers

# Four Athletes

Alan, Brian, Charlie and Dave took part in a running competition. There were no ties.

Alan said: "I'm second, and Brian is third."

Brian said: "I'm second, and Charlie is last."

Charlie said: "I'm third, and Dave is second."

Dave said: "I'm third, and Alan is first."

However, each person made one true statement true and one false statement. Can you determine which place Charlie ran?

Alan said: "I'm second, and Brian is third."

Brian said: "I'm second, and Charlie is last."

Charlie said: "I'm third, and Dave is second."

Dave said: "I'm third, and Alan is first."

However, each person made one true statement true and one false statement. Can you determine which place Charlie ran?

### Hint

Look carefully.### Answer

Alan, Brain and Charlie each made a statement about who ran second. However, only one person could run second, therefore, at least two of these three statements must be false.Hence, their other three statements must have at least two true ones: "Brian is third", "Charlie is last", and "Charlie is third". Obviously, "Charlie is third" must be false, and Charlie must be last.

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## Comments

I see how you got your answer, but you gave the information "each person made one true statement true and one false statement." I do not think either of Dave's statements are true.

There is a problem with the premise of this teaser (each person making one true and one false statement). Charlie's position can be determined by using only Alan's and Brian's statements. If Brian's first statement is true, it would contradict whichever of Alan's statements is true (Alan and Brian can not both be second, Brian can not be both second and third). Therefore, Brian's second statement must be true (Charlie finished last). Charlie's first statement, if true, would contradict Brian's true statement, so Charlie's second statement must be true (Dave finished second). Dave's first statement, if true, would contradict Charlie's true statement, so Dave's second statement must be true (Alan finished third). This leaves Alan with two statements that can not be true (Alan can't be second, and Brian can't be third).

Oct 31, 2008

I agree with the previous comment. Stated slightly differently, Charlie finishing last implies the following: Charlie's first statement is a lie => Dave finished second => Dave's first statement is a lie => Alan finished third => Alan's first statement is a lie => Brian finished third (contradiction with Alan finishing third). Any possible placing of Charlie results in a contradiction which proves there is no solution to the problem.

I agree with Joseph. I started out testing Alan's first statement as true. This caused a contradiction, so I made his first statement false. However, that makes a contradiction when you get to Dave's statements.

I concur with the above solvers; I honestly couldn't figure out where I was going wrong, because I kept turning up no possible solution. There is no possible way that all four racers could have finished, and each one have exactly one true statement.

I would have voted it Fun had it been actually solvable, but as it stands, my vote is a resounding Boring. I don't like unsolvable puzzles.

Better luck next time!

I would have voted it Fun had it been actually solvable, but as it stands, my vote is a resounding Boring. I don't like unsolvable puzzles.

Better luck next time!

I agree that this teaser is flawed.

That's 0 for 2 because shengiang's other similar teaser "Eight People" is also flawed. This teaser has no solutions, the other one has two solutions, so I suppose it all averages out to one solution each.

A correction would be:

Dave said:" I'm last and Alan is First"

Dave said:" I'm last and Alan is First"

I tis all correst except for Brians comments. if you write down 1st 2nd 3rd and 4th and then everyones names next to them that the 4 people are suspecting then first and last has to be Dave and Charlie because they were the only people there so it must be true which means their other comments must both be wrong leaving Alan in second and Brian in third. The only thing was Brians comments but you can get the answer...

I don't like flawed puzzles either. I arrrived at the correct answer before I looked at the comments. After looking though you realize that the whole point is to use the logic which I managed to bypass. Good catch on the flaw and if anyone sees this I came up with a second answer to his eleven up puzzle.

This teaser is inconsistent, there is no way each person makes one true statement and one false statement.

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