This is a comparatively straightforward guide tiling puzzle. In truth the tiling is all completed for you, you simply should specify what number of of every of the 26 given tilings to make use of. The puzzle is:
Using N full units of tetrominoes, tile N 4×5 rectangles in such a manner as to minimise range of items throughout the N rectangles. Score your set of rectangles by calculating the common variety of distinct tetrominoes in every rectangle. Find the smallest N that leads to the smallest attainable common rating. Here is an inventory of all of the methods to tile a 4×5 with tetrominoes (just one tiling proven for every distinct set of tetrominoes):

A parity consideration prevents a whole tiling for all odd N, so N can solely be even.

Here is an instance for N=4, ie tiling 4 4×5 rectangles with 4 units of tetrominoes. The range scores are 2,2,3,2 summing to 9 which is a mean rating of two.25 (NB this isn’t minimal for N=4)

A pc program will make quick work of this, however I think that many individuals will discover the reply by hand faster than by writing a program.