This is the sixth match in our group stage: from Group 2, it’s Jorge Nuno Silva up against Sameer Shah. The pitches are below, and at the end of this post there’s a poll where you can vote for your favourite bit of maths.

Take a look at both pitches, vote for the bit of maths that made you do the loudest “Aha!”, and if you know any more cool facts about either of the topics presented here, please write a comment below!

Jorge Nuno Silva – The roots of perfection

Jorge Nuno Silva is a Portuguese mathematician (PhD UCBerkeley 1994), President of Ludus and Professor at the University of Lisbon (Department of History and Philosophy of Science). He is an editor of Recreational Mathematics Magazine and Board Game Studies Journal.

Sameer Shah – What are the odds?!?

Sameer Shah has been teaching high school math in Brooklyn for the past twelve years. You can read his musings about his classroom at Continuous Everywhere but Differentiable Nowhere. He’s @samjshah2 on Twitter.

At my school, our senior class had 100 students in it. About a month ago, they graduated and I’m sad about that. They were wonderful. You see, I had a diabolical plan to keep them all at my school for another year. I rounded them up and asked them to play a little game. They were up for it, signed the permission form, and then I cackled. I told them that they should always read the fine print, and the permission form said if they didn’t win this game, they would have to stay for another year. BWAHAHAHAHA!

The game was a cooperative game. I assigned each student a number from 1 to 100. Then in their hundred lockers, I put slips of paper numbered 1 to 100 in them. But randomly. So student #1’s locker might have a slip of paper that says 42.

All students would line up outside the school. One by one, a student would be let in. That student would get to open 50 of the 100 lockers. If they opened the locker with their number in it, they were deemed successful and left the building. (During their time in the building, students couldn’t move the numbers around or do anything untoward like that. They simply were allowed to open up to 50 lockers and look.) I would close all the lockers, and then allow the next student in. If even a single student didn’t open the locker with their number in it, the entire senior class would lose, and they would have to stay with me for another year. 

I thought I had them. I mean, each student has a 50% chance of finding their number, and there were 100 students doing this, so the chance of success was (1/2)¹⁰⁰ ≈ 0.0000000000000000000000000000008

But this senior class, man, I tell ya. They are a bunch of clever ones. Believe it or not, they banded together and came up with a strategy that allowed them to graduate. Now it turns out their strategy didn’t guarantee they’d succeed. They had a 31% chance of success with it. But that is way better than ≈ 0.00000000000000000000000000008% chance of success I thought they’d have. 

So your challenge? It’s twofold. First, see if you can find any strategy that improves the (1/2)¹⁰⁰ odds. Second, see if you can find the optimal strategy that my students discovered

I first heard this problem at a workshop at a math teacher conference. It entranced me because it upends what seems impossible. It also ties together some beautiful pieces of mathematics. What I love is that it is also modern. A variant of this problem was first posed in 2003 by computer scientists. That’s not so long ago — it’s when I graduated college! Or wait, does this make me old? Whatever! It’s stunning and relatively new. Math doesn’t stop surprising us!

I secretly was hoping to build a little applet for y’all to be able to try out your strategies, with an array of digital lockers you get to open. But then I realized I have no idea how to program or build an applet. And then I was going to outline the optimal solution. BUT Y’ALL! The internets are magical! The youtube channel Minute Physics already made a video sharing the problem

And then shared a beautiful unfolding of the optimal strategy

The wikipedia page is also wonderful and gives a lucid explanation of the mathematics behind the strategy

So, which bit of maths do you want to win? Vote now!

 Loading ...

The poll closes at 9am BST on the 7th. Whoever wins the most votes will win the match, and once the group stages are over, the number of wins will determine who goes through to the semi-final.

Come back tomorrow for our seventh match of the group stages, featuring Sophie Carr and Sunil Singh. Or check out the announcement post for your follow-along wall chart!