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 Solution
- A 4 x 4 grid board has 16 squares, so you need to use four
T-tetrominoes to cover it. One way to do this is shown here
with the four T-tetominoes in different colors.
- A 5 x 5 grid board has 25 squares. Six T-tetrominoes would
cover 24 squares and seven T-tetrominoes would cover 28 squares.
We can't cover just 25 squares.
- View the 6 x 6 grid board colored as a checker board with
black and white squares.
A T-tetromino would cover 1 white and 3 black squares ( )
or would cover 1 black and 3 white squares ( ).
Since half the grid squares are black and half are white, a
cover would need half the T-tetrominoes covering 1 white and
3 black squares and half covering 1 black and 3 white squares.
A 6 x 6 grid contains 36 grid squares and would need 9 T-tetrominoes
to cover it (4 x 9 = 36). But 9 is an odd number and can't be
divided in half (with whole numbers) so you can't cover a 6
x 6 grid board with T-tetrominoes.
Back to Math Mountain
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