Cookie Culprit

One of Red and Ross must be telling the truth, since Jess either did steal or did not steal the cookie.

One of Jess and Sky must be telling the truth, for the same reason. That accounts for both truth tellers.

Therefore, Barney must have lied. So Sky stole the cookie.

Jess accused and Barney countered.
Red accused and Ross countered.
These above account for 2 truths and 2 lies spoken. The third lie can only be Sky's "I did not steal the cookie".

==> Sky stole the cookie.

Notice, only Jess and Sky are being accused of being the cookie thief. Assuming Jess is a liar, this means that Sky did not steal the cookie, and hence, Jess stole the cookie. If anyone is to claim that or imply that Jess did not steal, it must be a liar speaking. Anyone who thinks Sky did not steal the cookie or that Jesse stole the cookie must be telling the truth.

Given these criteria, Jess and Ross are the only liars. This is an issue because the problem stated there are 3 liars. Therefore, it must be false that Jess is lying, since there are only two options: 1) Jess is telling the truth or 2) Jess is lying. It can't be both, by the law of non-contradiction. So, we ruled out that Jess is lying, so she must be telling the truth, which means Sky definitely stole the cookie.

So notice, the only truthtellers are Jess and Ross. Sky, Red, and Barney are liars! 2 truthtellers and 3 liars fits the criteria of the problem and it's the only other alternative available.

What really narrowed down this problem was the constraint that there are 3 liars and 2 truthtellers and that there were only two people in question to be the cookie thieves. If there were 3 potential thieves, I wonder how this problem would have worked out.

Since Sky and Jess are the only names mentioned I just counted votes. Three people said it was Jess, two people said it was Sky. Two people told the truth so that must be the two that said it was Sky.