How to calculate the time it will take to solve a jigsaw puzzle Is there a way to know how much time it would take to solve a jigsaw puzzle if I already solve this same puzzle with a different number of pieces while timing myself?

Example of a landscape puzzle: (number of pieces) time to solve mm:ss   


(24) 00:50
(54) 01:58
(96) 04:51
(150) 09:07
(384) 45:16


If the same puzzle was available in a 1000 pieces format, how long would it take me?

Also, is there a minimum number of puzzle of different size I need to complete to get a formula? 

The image can greatly impact the time it will take to solve it too. If I am solving a puzzle with 2/3 of the image being a gradient sky and an image of a person, the gradient sky would take almost the same time as the person in a smaller puzzle size, but would take considerably longer the more pieces there are.
As you mention in the last paragraph, the time depends on the content, so there is no univocal relation between the number of pieces and the time.

Your data points are fairly well fitted by a linear law, and very well by a quadratic one. But we have no reason to believe that the time is super-linear, as you essentially build local aggregates of pieces and the time to locate one is roughly constant (or a slowly growing function of the total counts).

If you really want to find a statistically meaningful model, with a measure of the spread, you will have to solve hundreds of puzzles, and the result will depend on the operator.
Best Guess given only the data provided (y axis in minutes, x axis in number of pieces). Red shows your actual data, and blue shows Mathematica's best guess. It is a quadratic function, if you care to know.