Domino Tiling Problem

Can you cover the 34 squares with 17 2x1 dominoes?

Here's a puzzle I was shown by my lecturer Professor Schofield back in Bristol, last century:

Make a 6x6 grid and remove two diagonally opposite squares so that you're left with 34 squares.  Given 17 two by one dominoes, can you cover the remaining area?  The illustration above shows one failed attempt.


S
C
R
O
L
L

D
O
W
N

F
O
R

T
H
E

S
O
L
U
T
I
O
N


Sorry peeps.  It's an impossipuzzle.  To see why apply a checker pattern to the squares:

18 black squares but only 16 white squares
The two removed squares were both white.  So there are fewer white squares than black ones.  But each domino placed covers exactly one white and one black square.  If you could cover it perfectly with 17 dominoes there would be the same number of black and white squares.  There isn't, so you can't!


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