A probably easier way to prove that can't e done if both a and b are odd: As you need an equal number of black and yellow Ts there need to be 4X black and 4X yellow squares. Each 2x2 contains 2 black and 2 yellow squares, so there need to be an even number of 2x2s in there grid but if both a and b are odd you wil have an odd number of 2x2s in the grid. Since even is not odd , that task is impossible.
If both a and b are odd then there is one more square of one of the colors. But each tile you add you will always add two more squares of one color so it is impossible. If a is not a multiple of 4 and b is a multiple of 8 is gets more interesting to prove.
My interview is tomorrow, thank you for all your help🙏🏻🙏🏻
@OliverGoodman-todd you got this 💪💪💪
A probably easier way to prove that can't e done if both a and b are odd:
As you need an equal number of black and yellow Ts there need to be 4X black and 4X yellow squares. Each 2x2 contains 2 black and 2 yellow squares, so there need to be an even number of 2x2s in there grid but if both a and b are odd you wil have an odd number of 2x2s in the grid. Since even is not odd , that task is impossible.
I had my interview and still watch these problems they are interesting
@vynxvfx I appreciate that! How did the interview go??
@@JPiMaths pretty well there was one hard question explaining all the forces in a mechanics question which I found tricky
Beautiful way of working this out! But what if the dimensions are axb? Is there a solution just as clever and simple as the one you showed?
If both a and b are odd then there is one more square of one of the colors. But each tile you add you will always add two more squares of one color so it is impossible.
If a is not a multiple of 4 and b is a multiple of 8 is gets more interesting to prove.