Point $P$ is located strictly in the interior of rectangle $ABCD$ such that $PA$, $PB$, $PC$, and $PD$ have distinct positive integer values. What is the least possible value of $PA+PB+PC+PD$?

(WRONG ANSWER: DELETED)

I suppose that it depends on your understanding of the word distinct.

In the context of this question, I would take it to mean different.

I was careless. I will attempt that again.

I will guess 15