At first I thought the solution for this problem was simple…maybe to you it will be, but it evades me at present.
I need to figure out how to calculate the completed percentage of a jigsaw puzzle. Here are some examples:
Say I have 25 (5 x 5) piece jigsaw puzzle. If I calculated it correctly, that would be 40 potential individual piece matches.
Now if I just figure how many connections have taken place and divide that by the full number, that should give me my percentage, right? Wrong—at least perceptually speaking the issue seems to be a little more complex than that.
Here's why. Take a look at this 4 piece puzzle being solved.
I can offer more complicated examples if needed (I realized that 4 pieces is overly simplistic).
I have been racking my brain but I don't seem to be coming up with a solution that addresses all of these issues.
Think in components instead of connections. Let's define a move to be when two components of the puzzle are connected, as in the picture below.
In a puzzle with $n$ pieces, you start with $n$ components (each piece is a component) and you are finished when there is $1$ component left (the entire puzzle), so the puzzle requires exactly $n-1$ moves. Then your progress will be $\frac{\text{pieces}\,-\,\text{components}}{\text{pieces}\,-\,1}$.