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Given an 8x8 Mboard ( top left piece missing), as given below in the image, and 21 trominoes, how can we proof that there exists a configuration where there will be no overlap after all trominoes are placed.
What I tried doing was - a 8x8 Mboard will have 63 squares, now $63 / 21 = 3$, ie. it is divisble. But recall a tromino is L-shaped, so just show that the total number of squares is divisble with the total number of trominoes really isnt telling much. I mean how do you account for the shape of the tromino in that case.
I actually manually plotted out a configuration but could only get up 20 trominoes to fit. I have no idea how 21 fits in, and how we can say that there will be no overlap.
The red squares are the squares that were blank. There are 3 of them, but how can we rearrange the configuration to included 21 trominoes. And more than that how can we say that there will be no overlap?