This was one of my favorite puzzles, though slightly difficult. Unfortunately I got only one correct answer this time, from Suman Saraf. Well done Suman!

The answer is “no”.

Look at the unusual coloring of the 10×10 board above. Please note that 52 of these are greyed out, while 48 are white. No matter how you place a 1×4 rectangular stone plate, it will always cover 2 grey cells and 2 white cells. Therefore if there was a way to cover the entire grid with 1×4 rectangular plate, one would need to have the same number of white and grey cells. But with our coloring, that is not the case.

Hope you all enjoyed the solution.