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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