How can I calculate jigsaw puzzle dimensions (height & width) in puzzle pieces?
I have a puzzle which consist of $3,000$ pieces (the paper inside the box says that because of technical reasons the actual size of puzzle differ from what is printed on the box, so the actual amount of pieces is 3008). Also, I know the actual dimensions of puzzle, when it'll be solved – cm 114.3x 82.3 (in 45" x 322/5"). All the pieces are slightly differ from each other in their dimensions, but they are about 1.5 x 1.5 cm each. I tried to find all edge pieces – counted 218 after all but I'm not sure that my puzzle is full and none of pieces is lost.
So is there any way to calculate perimeter in pieces and to know width and height in pieces?
Best Answer
$3008 = 64 \times 47$, which is the only decomposition that makes sense here ($47$ being prime). Each piece will then be, on average, $1.79\mathrm{cm} \times 1.75\mathrm{cm}$.
You should have $4$ corner pieces and $214$ edge pieces.