# One Hundred Factorial – the puzzle and the event

The weekly puzzle session that I run at the University of Adelaide is called One Hundred Factorial. In the middle of the night, I suddenly realised that I have never written about why it is called One Hundred Factorial, and so here is the story.

The very beginning

Once upon a time I was a PhD student in the School of Mathematical Sciences at the University of Adelaide. Sometime during the third year of my PhD program (2007), I was asked to give a talk to the first year undergraduate students as part of an evening event where the goal was to hopefully convince them to keep studying maths at a higher level next year. I titled my talk “How to Tell If You Are a Mathematician”. I don’t remember any of the things I spoke about, except for one thing. Before I started talking, I put a puzzle up on the document camera. I did not mention the puzzle in any way or look at the screen at all. I just did my little talk as if it wasn’t there. But right at the end of my talk I said this:

The final and truest way to tell that you are a mathematician is that you haven’t been listening to any of what I just said, and instead have been trying to solve this puzzle.

Cue guilty looks and nervous laughter from all of the academic staff in the audience, which successfully proved my point. Anyway it worked. Several students came up to me to talk about the puzzle, and I was able to direct them to lecturers who could talk to them about their study options. Yay for puzzles, right?!

This was the puzzle I used so neatly to make my point about the mathematician’s mind:

The number 100! (pronounced “one hundred factorial”) is the number you get when you multiply all the whole numbers from 1 to 100.
That is, 100! = 1×2×3×…×99×100.
When this number is calculated and written out in full, how many zeros are on the end?

I don’t remember where I got the puzzle from, but it is a pretty famous one that’s been around for some time. I actually hadn’t even thought through a solution at the time either. I just knew that it mentioned a concept that had been in the first year lectures recently.

The puzzle sessions begin

The other thing that happened that night was that a group of students and staff stood at the blackboard in the School of Maths tea room to nut out a solution to the 100! puzzle. I can’t even remember if we finished it or not, but we did decide that we should get together regularly to solve puzzles together, and a weekly puzzle session was born. At the first session, we started with the 100! problem again, and an extension of it, which is to find out what the last digit is before all those zeros start. Then as the weeks went on, we would do puzzles that I would find and bring to the sessions.

When I finished my PhD in mid-2008 and took up the job in the Maths Learning Centre, I took my little puzzle session with me, and was able to invite more students to come along, and it slowly morphed into a student event more than a staff event, which really pleased me. In fact, a regular at these puzzle sessions for years was that first student who had come up to me after my talk at the first-year event, and he eventually became one of my tutors at the MLC.

The name of the event

Over the years the puzzle session has had many names. We started out calling ourselves “People with Problems”, and then simply “Puzzle Club”. For a while it was called “The Hmm… Sessions” after the sound we made very often while thinking about puzzles. Indeed, there is a reference to the Hmm Sessions inside this very blog. But in 2012 after the website where I was hosting our online discussion was decommissioned, I decided it was time to change the name. I was also starting to think about moving the sessions out of the MLC itself and into a public space, and to match with this move I wanted a new name. I thought long and hard, and decided to name it after the first puzzle we ever did, the puzzle that first inspired staff and students to talk and think about maths together, the puzzle that helped students decide they really were mathematicians after all.

The legacy

So the regular puzzle session of the MLC became One Hundred Factorial at the end of 2012, and here we are in 2020 still going, so that now it’s been One Hundred Factorial longer than it’s been any other name. It’s been my testing-ground for new puzzles and games and teaching ideas, a place where I have made friends and welcomed people from around the country and the world. And it has become a glowing island of mathematical play in the middle of the stressful university life, and indeed the middle of a stressful life generally. In recent weeks it is a glowing island of community in a world of pandemic-induced isolation.

One Hundred Factorial reminds us that there is always something joyful to think about if you are looking for it, and that it’s okay to pause and ignore your responsibilities for a while to think about it, and that doing this with people is a source of shared joy. I hope the puzzle and the event can keep reminding us of that for a long time yet.

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