Our Red Frog wants to get to the Orange Frog, but he can only jump right and down, but over multiple lilies if he chooses, although he can't stay still.
How many ways can he do it?
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I completed mine similar to Raystafarian. I determined how many paths you can take to get to each pad. I started with A and found 1 path. The B, with another 1 path. THen when I look at something like D, I see it can be reached from A or B. Add those together, you have 2 paths to reach D. Continue down the chain until you find the final value for L.
My picture also includes the assumed jumps I can make. I assumed that jumps were not possible unless the middle is clearly down and right. So jumps C-D and B-H were not possible.
The program does the calculations for me. So if I HAD allowed the the other jumps, I would have gotten these values.
CD allowed yields 82, BH allowed yields 79, CD and BH yields 87.
It matches f"s answer, but I wanted to include the alternates and have a spreadsheet to show that it can be reduced to spreadsheet with set equations. Give me any number of lily-pads and define the limits and this will solve it.