Summer Challenge 2005
5D Wong Hin Yeung
(1) 4:24 or 7:36 am/pm
(2)
First, it can be shown that a larger L-shape with 2-unit thick can be covered with 4
L-shaped tiles.
}2-unit thick
Moreover, an L-shaped floor with 4-unit thick can also be covered with 4 2-unit thick
L-shaped floors, which can be further covered with L-shaped tiles.
Similarly, an L-shaped floor with 2n-unit thick can be covered with 4 2n-1-unit
L-shaped floors, which can also be covered with the tiles.
Therefore, we conclude that any 2n-unit thick L-shaped floor can be covered with
1-unit thick L-shaped tiles.
Now, we consider the floor which is going to be covered.
It composes of 2n x 2n squares with one of the squares removed.
For example,
We divide the floor into 4 smaller squares.
In the 2n-1 x 2n-1 square where the removed square is located, we further divide it into
4 squares.
Note that the remaining three large squares form an ‘L’.
Repeat the above step until the divided square contains the removed square only.
Now, we have divided the whole floor into n L-shaped floors.
Since we have conclude that all 2n-unit thick L-shaped floors can be covered with the
tiles, the whole floor with one square removed can also be covered with the
L-shaped tiles.