How to calculate the number of pieces in the border of a puzzle? Is there any way to calculate how many border-pieces a puzzle has, without knowing its width-height ratio? I guess it's not even possible, but I am trying to be sure about it.
Thanks for your help!
BTW you might want to know that the puzzle has 3000 pieces.

Assume that the puzzle is a rectangle of $a\times b\ $ cm$^2$, and the pieces can be idealized as rectangles of $c\times d\ $ cm$^2$. Then $m={a\over c}$ pieces border along an $a$-side and $n={b\over d}$ pieces along a $b$-side. You have told us that $m\cdot n=3000$, and you want to know the number $N:=2m+2n-4$. We don't have enough information to determine $N$. By the AGM-inequality one has ${m+n\over 2}\geq \sqrt{mn}$. This implies the estimate $N\geq216$.
