Congratulations to Jonathan Inbal for giving the best solution to this month's problem. He correctly answered parts 1 and 2 of the problem and gave a partial answer to part 3. His solution is posted here.

A tetramino is a planar figure consisting of four squares joined along common edges. (Think of Tetris pieces.) Up to rotations and translations in the plane, there are exactly seven distinct tetraminos, which are pictured below.

This month's problem is about whether or not a rectangular piece of graph paper can be cut into pieces, each of which is a "T" tetramino (the shape on the far right in the figure above). Each piece must be cut along the lines of the graph paper, but you can rotate the pieces however you like. For example, if you start with a rectangle which is two squares high and five squares wide, it is impossible to cut it into "T" tetraminos. Any attempt to do so will have at least two squares left over.