# Tile Covering

Discrete Mathematics Level pending

You have a horizontal strip length $$N$$ and width $$1$$. You have infinite supply of $$1 \times 1$$ tile and $$2 \times 1$$ tile. You plan to cover the horizontal strip with these two types of tiles.

If $$N$$ is 1, you can cover the strip in only one way.(placing a $$1 \times 1$$ tile). For $$N = 2$$, there are two ways, placing two $$1 \times 1$$ block or placing one $$2 \times 1$$ block.

What are last three digits of the number of ways to cover a horizontal strip of length 23 ($$N = 23$$)?

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