Following up on Matt Enlow’s Fibonacci problem

About a week ago we took a quick look at a problem that Matt Enlow had posted on twitter:

Matt Enlow’s Fibonacci Problem

We had a little bit of extra time this morning, so I decided to revisit the problem to talk a little bit about modular arithmetic. I also really like this problem as an introductory proof problem, too, but that’ll have to wait for another day.

Also, sorry for writing the problem backwards at the start of the video, we manage to straighten it out once we look at the Fibonacci numbers mod 8.


Once we looked at the numbers mod 8, it was time to look at them mod 9 and see if we saw a pattern. I’d like to revisit this project some time to talk about ideas like why 8 = -1 mod 9.


So, I think this is a great problem for kids. It asks about a property that is fairly easy to understand and also provides a nice opportunity to introduce modular arithmetic. Lots of opportunities here to have some fun math conversations 🙂

What would you say?

Sometimes I get asked for numbers at work in situations where I have next to no information. Here’s a good example from today:

A company is looking to buy protection against an event which we believe happens once in ten years. I do not know how we arrived at the 1 in 10 year number, or even when we came to believe in that number, or, as I think about it, even it was actually us who believed in that number. In any case:

Year 1: Event happens
Year 2: Event happens
Year 3: Event happens

The question to me was – what do you think the probability of the event happening in year 4 is? There’s little to no math or calculation you can do here – there are only two pieces of information:

(a) At some point someone believed that the event happened once in 10 years.
(b) That event has happened in each of the last 3 years.

That’s all you know . . . so what’s your answer to the question?