We have two kind of tiles : 1 x 1 and 2 x 2, and use them to cover the 8 x 3 road without overlapping, how many different ways to arrange tiles there?
5 answers
46
It is not the right answer, unfortunately.
well, using 24 1x1 tiles is one way.
Using 2x2 tiles, only one tile will fit across. It can be on the left or right side.
So, a single 2x2 tile can be placed in 2x7=14 places.
Now consider using more than one 2x2 tile. Figure how many places it can slide around into. I'm sure you can work it out.
Only a maximum of 4 2x2 tiles can fit into the road.
Using 2x2 tiles, only one tile will fit across. It can be on the left or right side.
So, a single 2x2 tile can be placed in 2x7=14 places.
Now consider using more than one 2x2 tile. Figure how many places it can slide around into. I'm sure you can work it out.
Only a maximum of 4 2x2 tiles can fit into the road.
Ok.
So for 2x2 2 tiles I got 16
for 2x2 3 tiles I got 24
and for 2x2 4 tiles I got 10
Finally, I counted up 65 ways. But it is still the wrong answer. Where am I wrong?
So for 2x2 2 tiles I got 16
for 2x2 3 tiles I got 24
and for 2x2 4 tiles I got 10
Finally, I counted up 65 ways. But it is still the wrong answer. Where am I wrong?
must use recurrence equation.
1 answer