Hi everybody!
My name is Jason Ermer and this is the first challenge video for the new blog
that I’m experimenting with called Collaborative Mathematics.
If you haven’t watched the How It Works video that explains the whole idea
behind this blog, you might want to check that out.
Since this is the first challenge video, I thought we would do a problem that
was sort of an introduction.
I’ll introduce myself to you by defining an Ermer Number.
And we’ll explore some things about Ermer Numbers.
An Ermer Number is a number that looks like my last name.
More specifically, it’s a five digit number
of the form e-r-m-e-r
where e, r, and m are distinct digits.
For example, the number 29,129
twenty-nine thousand one hundred twenty-nine
that’s an Ermer Number.
40,740 is an Ermer Number.
But the number 60,206 sixty thousand two hundred six
that’s not an Ermer number.
And 12,345 twelve thousand three hundred
forty-five that’s not an Ermer Number either.
So, having defined which numbers are Ermer Numbers and which are not, the
core challenge this time is:
How many Ermer Numbers are even?
So if you can answer that question and explain your solution, then great!
Go ahead and upload your response video!
If you can answer the core challenge question, you might be interested in
thinking about some other questions that come to mind.
For example we’re talking about even Ermer Numbers.
You might wonder how many Ermer Numbers are multiples of three.
How many are multiples of 7?
There’s all sorts of questions just like that.
What’s the smallest distance between two consecutive Ermer Numbers?
What’s the smallest difference between two consecutive Ermer Numbers?
What’s the largest difference between twoconsecutive Ermer Numbers?
Are there any Ermer Numbers that are prime? What sort of properties
would they have?
In addition to being prime, I mean.
Anyway there’s a lot of questions that might come to mind. If you discover
other interesting properties of Ermer numbers
or if other questions come to mind -- whether or not
you can answer them -- it’s cool if you just
put those in your response video so that we can all think about them.
Okay! There it is! Go have some fun and do some math!
And check us out online.
We’re at collaborative mathematics.org
You can find us on Facebook and Google Plus.
You can follow us on Twitter.
You can subscribe to the YouTube channel.
All those things might be things you want to do.
Otherwise, I look forward to seeing what happens next!