#22 - Local

[Administrator]

Complete Question Explanation

The correct answer choice is (D).

Answer choice (A):

Answer choice (B):

Answer choice (C):

Answer choice (D): This is the correct answer choice.

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[rwitt09]

What would be the most efficient way of going about this question? It seems time consuming for the last question of the section.

[Jeremy Press]

Hi rwitt,

Saw your question and have always thought this game was interesting, so here are a couple thoughts!

First, you could approach this game from the start using some rough global templates (I see four rough global templates), based around what can be in number 3 (only F or T) and whether the F or T in number 3 is the same as the hat in number 1 or not. Even though there are four global templates, there are only two of those that this local condition fits within. From there, it's pretty easy to compare each answer against those two templates to see if it will work or not.

But, there's also a simple enough way to get to the correct answer without using templates. The local condition of having P in number 4 activates the contrapositive of the fourth rule. That means that number 1 and number 3 must be the same kind of hat (if they were different kinds, you'd have to have a T in 4). Since number 2 and number 5 must also be the same kind of hat, that means there can't be any more P's (since anywhere you'd put P in addition to number 4 would require two more P's, either in 1 and 3, or in 2 and 5, and there are a max of 2 P's allowed by the first rule). This eliminates answer choice B.

So, only F and T are available to fill spaces 1/3 and spaces 2/5. They can fill those spaces in any combination of F and T: all F's, all T's, or 2 of each). But that means, no matter what, there will be an even number of F's and T's, which eliminates answers A, C, and E automatically.

Hope this helps!