Michael Samuels
11/28/06
Math 051
Extra Credit
1.
Given a 100x100 grid with 2x1 tiles.
Punch out the top left and bottom right and
prove that you CANNOT cover the grid
If each square (1x1) on this grid is one of two colors, for example blue and red, the
colors would alternate on the grid for the purposes of this proof.
(RBRBRBR > 100)
Since each tile covers 2 squares, it must cover both a blue and a red square.
If the top left and bottom right squares are removed, you would be removing two
red squares.
Since each tile must cover a red and blue square, if there are now two
less red squares, you will not be able to fill the grid.
Red MUST equal blue in order
for it to be covered, and since there are more blue then red with the two corner
squares gone, the grid cannot be covered
2.
Given a 99x99 grid with 2x1 tiles.
Punch out the top left square.
Can this be
covered?
In order to form the 99x99 grid, you must remove the 100
th
row, which removes the
same amount of each color, but since Red is the corner it would be counted in vertical
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