My teacher gave us a riddle that goes like this:
You have a $7\times 7$ square and $16$ $3\times 1$ tiles. Of the $16$ tiles, $15$ are straight and $1$ is crocked ("L" shaped). When you tile the square with these tiles you should get that one unit is left un-tiled (because $7 \times 7=49$ and $16\times (3\times1)=48$).
The question is in what locations can the un-tiled square be?
Keep in mind that you can rotate the pieces.
I've never saw this kind of questions before so I'm not sure how to go about solving something like this. I tried to check some positions and it seems that the "L" shaped tile cannot be placed in the corners, but I don't know how to continue...
Any help will be appreciated because this is driving me crazy. Thanks.