Rearranging a Staircase Grid into a Square

Question

Is there any way to rearrange the above "staircase" grid into three pieces that can be rearranged into the 6x6 square grid below it? I have tried this problem for over six hours and have not arrived at any solution. There has to be some general strategy in approaching this problem other than brute force, right??

I would appreciate any and all help--hints, suggestions, anything... I've gone mad trying to solve it

:(

Answer 1

$$\def\r{\color{red}{1}}\def\b{\color{blue}{2}}\def\g{\color{green}{3}} \matrix{\r\cr \r&\r\cr \r&\r&\r\cr \r&\r&\r&\r\cr \r&\r&\r&\g&\g\cr \r&\r&\r&\g&\g&\g\cr \b&\b&\b&\g&\g&\g&\g\cr \b&\b&\b&\g&\g&\g&\g&\g\cr}$$ can be rearranged as $$\matrix{\g&\g&\g&\g&\b&\b\cr \g&\g&\g&\g&\b&\b\cr \g&\g&\g&\r&\b&\b\cr \g&\g&\r&\r&\r&\r\cr \g&\r&\r&\r&\r&\r\cr \r&\r&\r&\r&\r&\r\cr}$$

Answer 2

You first the 6 by 6 on the staircase. Even thought it is not total, you can take the left over pieces and do it.