This is a relatively easy manual tiling puzzle. In fact the tiling is all done for you, you just have to specify how many of each of the 26 given tilings to use. The puzzle is: Using N complete sets of tetrominoes, tile N 4x5 rectangles in such a way as to minimise diversity of pieces across the N rectangles. Score your set of rectangles by calculating the average number of distinct tetrominoes in each rectangle. Find the smallest N that results in the smallest possible average score. Here is a list of all the ways to tile a 4x5 with tetrominoes (only one tiling shown for each distinct set of tetrominoes):
A parity consideration prevents a complete tiling for all odd N, so N can only be even.
Here is an example for N=4, ie tiling four 4x5 rectangles with four sets of tetrominoes. The diversity scores are 2,2,3,2 summing to 9 which is an average score of 2.25 (NB this is not minimal for N=4)
A computer program will make short work of this, but I suspect that many people will find the answer by hand quicker than by writing a program.