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Logical Choice (Posted on 2013-12-05) Difficulty: 3 of 5
Ms. Cooper was teaching a logic class which is very always popular with students and this semester was no exception. There was only one space left in the class and three students had applied. Each of the applicants was interviewed. The last space must be taken by a student who makes either three true or three false statements. One of the other two applicants makes two true and one false statement. The other applicant makes one true and two false statements.

Here's what the three applicants said during their interview:
Keith:
1. Cade is the oldest.
2. Kenny will not bring the teacher an apple.
3. I am the one with three true statements.

Kenny:
1. I would bring the teacher an apple.
2. Cade will be chosen.
3. Keith's first statement is false.

Cade:
1. I am the oldest, so I should be selected.
2. Kenny will be selected.
3. Kenny's third statement is true. 
Which student was selected as the last person chosen for the logic class?

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution liars sometimes prosper (spoiler?) | Comment 2 of 4 |
The proposed solution in the first post does not seem to work.  If all of Keith's statements are true, then all of Kenny's are false.

Further, all of Kenny's cannot be true, because then Kenny is selected, and this makes the 2nd statement false.  Cade does not make three true statements, for the same reason.

Therefore, the last place is taken by somebody who tells three lies.  Could it be Keith?  If Keith tells three lies, then Kenny's statements are TFF and Cade's are FFT.  So that is a solution.

Is it the only solution?

If Kenny tells three lies, then Keith's statements are ?TF and Cade's are ?TF.  This could work, If Cade is the oldest.  Keith's statements are then TTF but it could be argued that Cade is FTF.  It is false, after all, that he should be selected because he is oldest.  That is, after all, not the selection criterion.  And I think that works as an alternative solution.

If Cade tells three lies, then Keith is T?F and Kenny is ?TF.  Since one of the ? is true and the other false, then this is also a solution.

SO, THE CHOSEN ONE CAN BE ANY ONE OF THE THREE.  ALL WE KNOW FOR SURE IS THAT HE TOLD THREE LIES.


  Posted by Steve Herman on 2013-12-05 14:14:37
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