It was time for celebrations in the Gryffindor common room. But as luck would have had it, Seamus miscued a spell setting the common room floor on fire. The students were evacuated quickly. Dumbledore was informed of this act and he thought of the perfect punishment for Seamus. He had to tile the common room without using magic (of course). The room was two units wide and N units long. Seamus was provided with two types of tiles: a rectangle that is one unit wide and two units long, and a L-shaped tile covering 3 square units. Pictures of the tiles are shown below. Seamus was allowed to rotate the tiles as he laid them. He had an unlimited supply of tiles. He however failed, and requested Harry to help. Harry said that he could only tell the number of different ways of tiling the room using these tiles. For instant, a2 xx 3 room could be tiled in 5 different ways as follows: Notice that the tiling could use both types of tiles. consider the tiling of a 2 xx 4 room below. Seamus then asks Harry for the number of different ways of tiling a room of dimension 2 xx 12. What would be Harry's answer?

It was time for celebrations in the Gryffindor common room. But as luc

1.	It was time for celebrations in the Gryffindor common room. But as luck would have had it, Seamus miscued a spell setting the common room floor on fire. The students were evacuated quickly. Dumbledore was informed of this act and he thought of the perfect punishment for Seamus. He had to tile the common room without using magic (of course). The room was two units wide and N units long. Seamus was provided with two types of tiles: a rectangle that is one unit wide and two units long, and a L-shaped tile covering 3 square units. Pictures of the tiles are shown below. Seamus was allowed to rotate the tiles as he laid them. He had an unlimited supply of tiles. He however failed, and requested Harry to help. Harry said that he could only tell the number of different ways of tiling the room using these tiles. For instant, a2 xx 3 room could be tiled in 5 different ways as follows: Notice that the tiling could use both types of tiles. consider the tiling of a 2 xx 4 room below. Seamus then asks Harry for the number of different ways of tiling a room of dimension 2 xx 12. What would be Harry's answer?
Answer» 1055 1255 1455 1450 Solution :For a `2 XX 10` room, Total WAYS of TILLING : 1255

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