This is an attemps to answer the question: Given a set of these, is it possible to form a rectangle using all the pieces.
Open index.html in a browser. Enter the number of pieces of each type you have, and the solver tries to solve the problem.
Currently, only if you enter 1, 2 and 4 do you get an answer in a reasonable amount of time.
In order to test with a subset of pieces, I have added an option in the url. The pieces are called SQR, T, SL (snake left), SR (snake right), L, NL (inverted L) and I. index.html?pieces=SQR-I uses only the square and the I pieces.
The following subsets give more results: tetris.html?pieces=SQR-I: even numbers, 1 and 3 tetris.html?pieces=SQR-I-L-NL: 7 and under
Opening basicTetrisChecks.html allows you to run some basic tests.