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Color the board like this: https://imgur.com/a/kuaeQJW https://imgur.com/a/kuaeQJW Note that each tromino covers one yellow square, one red square and one gre
by avnerium 8y ago
Color the board like this:
https://imgur.com/a/kuaeQJW https://imgur.com/a/kuaeQJW
Note that each tromino covers one yellow square, one red square and one green square. Also, there are 21 yellow squares, 21 green squares and 22 red squares, so the square which will be left must be red.
Now flip the coloring of the board horizontally:
https://imgur.com/a/U7bnATI https://imgur.com/a/U7bnATI
and again there is (obviously) one more red square than yellow squares and green squares. The square which will be left empty, should be red in both of the colorings (the original coloring and its reflection). The only squares that satisfy that, are (3, 3), (6, 3), (3, 6) and (6, 6).
- tromp 8y agoPrecisely!