## Friday, August 10, 2012

### Brain Teaser 10

Got this one from  http://www.edcollins.com/logic/.  It is a short one, so you don't have to dedicate much time to it.

The Three Suspects

Kyle, Neal, and Grant were rounded up by their mother yesterday, because one of them was suspected of having grabbed a few too many cookies from the cookie jar. The three brothers made the following statements under very intensive questioning:
Kyle: I'm innocent.
Neal: I'm innocent.
Grant: Neal is the guilty one.

If only one of these statements was true, who took the cookies?

The easiest way to solve this is to make a grid and test the possibilities:

F    T    F
Kyle - I'm Innocent     T     F    F
Neal - I'm Innocent     F     T    F
Grant - Neal is Guilty  F     F    T

Using the above analysis, Kyle is the culprit.

This answer agrees with the one from Ed Collins' site, but one thing I noticed is that concluding that the third column is false is somewhat open to interpretation.  The original question says that "one of them was suspected of having grabbed a few too many cookies."  The way this is written suggests that we are supposed to only have one culprit but if it is a true unknown, then can't there be two (or even three) thieves?  If this possibility is allowed, then couldn't column three also be correct.  If Kyle and Neal both took extra cookies then their statements are false.  Grant said that "Neal is the guilty one" but does not including Kyle make his statement false.  I don't think so, but I guess it depends on how it is read.

Anyway, at this point I am babble typing so I will stop now.