By David Rice
Executive Director, Public Ed Works

WINCHESTER, Va. (March 23, 2024) – The following is an exchange this week between my high school English teacher and my high school math teacher.

I still recall how the math (trig) teacher labeled points on a circle with the letters of his daughter’s name. And I still hear from the English teacher pretty much every day. (He reads a lot of British newspapers.) I am astounded that they keep in touch and I still learn from them, 40+ years later.

They care that much.

And that’s what makes a teacher.

Just follow the back-and-forth – even if you don’t follow the math. And please appreciate the folks who teach us and teach our kids.

English Teacher:

With the NCAA brackets announced and March Madness officially upon us (and spilling into April), news broadcasts (not just sports reports) are full of advice on how people should fill out their brackets.

I saw one of these fluff reports yesterday featuring a math professor from the University of Miami. 

He claimed that there are 9 quintillion possible ways to predict the outcome of the NCAA tournament. That’s a pretty huge number.

Also, he said that number is “comparable to the grains of sand on all the beaches in the world.” That comparison seemed like a stretch.

So I decided to check with the person I trust most regarding all things math: my former colleague from Handley High School. I really enjoyed the time he took to explain the math involved and thought you might, too. 

Math teacher:

I wondered if you just wanted the answer to your question or if you wanted an explanation.  The teacher in me (and I know, the teacher in you) wants to know how and why, so here is the explanation.

For the bracket, there are only 63 games (they don’t count the four play-in games).  Each game has two possible outcomes. In two games, there would be 2 x 2 = 4 possible outcomes. If Team A and Team B play in the first game and Team C and Team D play in the second game, here are the possible outcomes (winners): A-CA-DB-CB-D

For three games, there are 2x2x2 = 8 possible outcomes.  Using Teams A and B, C and D, and E and F, here are the outcomes: A-C-EA-C-FA-D-EA-D-FB-C-EB-C-FB-D-EB-D-F

Hopefully, that makes sense — I thought it would be good to see actual possibilities before we generalize.

In the 63 games in the bracket, there would be

2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 2^63 possible outcomes.

Here is the answer for 63 games (and also the answer if they counted the play-in games – 67 games):

2^63 = 9,223,372,036,854,775,808

2^67 = 147,573,952,589,676,412,928

So, the Miami prof was right – it is over 9 quintillion ways.

As far as the sand metaphor goes, I would guess that it is true. My mind can’t even fathom what a quintillion looks like, but it is huge – it is 1 trillion times 1 trillion, but that doesn’t really help.