|
It was a constructive proof.
Basically, the defective row forces a partition of the next row because it has a run of odd length starting from an odd column. I called this a class D row.
The next row is partitioned into two runs of odd length, both starting from even columns. Because both runs are odd length, this forces the next row to be partitioned by two dominoes. Because both runs start from even columns, the next row must have a run of odd length starting from an odd column. I called this a class P row.
As you can see, all P rows are followed by D rows, while all D rows are followed by P rows. Couple this with the fact that both rows must have, at least, one domino jutting up from them, this shows that no tiling of this shape exists...
QED
|