Whose hat was taken by P, how and why?

Question

Four brothers go to a dance party. As the leave,each of the brother accidentally takes a hat belonging to another brother and the coat belonging to the third brother. M takes the court belonging to the brother whose hat is taken by P, while P's coat is taken by the brother who takes M's hat. S takes J's hat. Whose hat was taken by P? ( Answer is S )

What's the technique of solving this question? Those "twists and turns", I don't get them. How can I put them to symbols or number so that I get it?

Answer 1

The trick is to use tables like the one below:

On the left are the brothers taking stuff. On the right are the brothers they are taking it from. We initially know that no brother takes their own hat or coat, so we fill in those cells with an "X". Now, the last clue ("S takes J's hat") is the most concrete, so we use that first:

Above we have filled in that S takes J's hat. When we know a cell is the correct choice, we can mark all other cells in that row and column with an "X". But we also know that if S took J's hat, he cannot also have taken J's coat, so we mark that cell with an "X".

Next, let's take the first clue, i.e. "M takes the coat belonging to the brother whose hat is taken by P". We see in the table that P could only have taken the hat of either M or S, so M could only have taken the coat of M or S. But M cannot take his own coat, so he must have taken the coat of S. And therefore P took the hat of S:

At this point we have actually already got the answer to the question of "whose hat was taken by P", without ever using the last clue! Still, let's continue. Notice that there are several rows and columns with only one free cell left. Those free cells must then be the answer and we can mechanically fill them in:

For completeness sake we can use the last clue to fill in the rest:

Answer 2

"Just" be systematic.

S takes J's hat, so takes P or M's coat. But P's coat was taken by someone who took M's hat, so can't have been taken by S; so by the previous fact, S takes M's coat.

So far, S takes J's hat and M's coat.

Consider J's coat, which cannot be taken by S or J so is taken by P or M. If M takes it, then J's hat is taken by P (by the first fact we were given) - but that's not allowed because we know J's hat is taken by S. So P must have taken J's coat.

Proceed in this vein. (I don't think I've made a mistake, but I was distracted about six distinct times while writing this.)