5. (10 points) A hare jumps in one direction along a strip divided into cells. In one jump, it can move either one or two cells. In how many ways can the hare reach the 12th cell from the 1st cell?

![](https://cdn.mathpix.com/cropped/2024_05_06_bc3593ebed90e6cb13c5g-1.jpg?height=208&width=971&top_left_y=1915&top_left_x=591)

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# Answer: 144

Solution. In each cell, we write the number of ways the rabbit can get there. In the first cell, it's 1, in the second cell, it's 1, and so on. In each subsequent cell, the number of paths the rabbit can take splits into two groups: the last jump is 2 cells or the last jump is 1 cell. Therefore, the number in the cell is the sum of the numbers from the two previous cells (this is the Fibonacci sequence).