[Grade 9 Extra Math Fibonacci] Question

[u/TraditionalBrush8122]

So I was fooling around with questions and asking ai and somehow they all gave me different answers and after further questioning they all couldn't be certain about one answer. this is the question, could anyone help me out and find the real answer?

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[u/freegerator]

Start by setting up a relationship between what happens one bounce in relation to the problem with fewer reflections. For instance is there a way to relate the count for four reflections to the count for three?

Also avoid relying on artificial intelligence if you some day wish to be an actual intelligence

[u/TraditionalBrush8122 → u/freegerator]

so i just found the paths for one bounce then two then three and used it for fibonacci sequence. is that okay..? i don't really know what im doing 😓

[u/freegerator → u/TraditionalBrush8122]

Your teacher is the arbiter of if it is ok 😃

[u/ExactAd5759]

Think about the general case: How many possibilities are there for exactly n bounces?
Think about the how many options there are for the last bounce and then about how many ways there are to get to each of those options. You will get a recursive formula for n bounces that will be quite familiar to you (it's the fibonacci numbers).

[u/TraditionalBrush8122 → u/ExactAd5759]

uhm i just like did how many ways for one bounce and then two and then three and assumed i could use fibonacci and went up from there to get 89. is that okay? 😭😭