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Mathematical Objects: Noughts and Crosses (Tic Tac Toe) board

Mathematical Objects

A conversation about mathematics inspired by a Noughts and Crosses (Tic Tac Toe) board, covering Noughts and Crosses, a surprising number of variants, with a bit of higher dimensions and topology for good measure. Presented by Katie Steckles and Peter Rowlett.

Noughts and Crosses board
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Mathematical Objects: Pile of matchsticks

Mathematical Objects

A conversation about mathematics inspired by a pile of matchsticks. Presented by Katie Steckles and Peter Rowlett.

Pile of matchsticks
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The Joy Of Winning documentary on BBC2

Hannah Fry presents a new one-off BBC4 documentary about game theory (reading the description, it sounds more classic than combinatorial), which the BBC4 website describes as a “gleefully nerdy adventure”. Should be fun!

This is tomorrow, 28th August 2018 at 9pm on BBC4 and on iPlayer after.

Update: iPlayer link to The Joy Of Winning.

New York Times puzzle is pure game theory

Image CC-BY Raymond Bryson, f-oxymoron on FlickrThe Upshot is a column in the New York Times based around analytics, data and graphics. (It was conceived around the time when Nate Silver left to work for ESPN). Earlier this week, managing editor David Leonhardt and data journalist Kevin Quealy posted an interesting puzzle, entitled ‘Are You Smarter Than 49,485 other New York Times Readers?’

The puzzle consists of a simple question – you need to pick a number between 0 and 100, and all 49,485 of the responses will be collated (assuming that every single one of the Times’ readership actually enters a number) and averaged. If your guess turns out to be the closest whole number to two-thirds of the average guess, you are clever and you win.

Programming to investigate Quarto

I was invited to contribute to a special issue of The Mathematics Enthusiast on ‘Risk – Mathematical or Otherwise‘, guest edited by Egan J Chernoff. I wrote about the Maths Arcade and programming strategies for a game we play there called Quarto. Really, I was sketching an outline of an idea to encourage student project work.

My title is ‘Developing Strategic and Mathematical Thinking via Game Play: Programming to Investigate a Risky Strategy for Quarto‘ and the abstract is below.

How to Win at Pointless

For the benefit of overseas readers, or British readers in full-time employment, I should briefly explain the concept of daytime TV quiz phenomenon Pointless. The pinnacle of British public service broadcasting, it’s shown at 5.15pm every weekday on BBC One and is hosted by Alexander Armstrong of comedy double-act Armstrong & Miller, and Richard Osman of comedy double-act Armstrong & Osman. We shall investigate how we can use maths to analyse the show, improve our chances of winning it, and ultimately perhaps improve the show itself.

The aim of the game is in each round to give the most obscure correct answer to a given question. Each question ($Q$) has a large set of valid answers $A_Q$, questions perhaps asking contestants to name “Films starring Bruce Willis” or “Countries without an O in their name”. All the questions have been asked to 100 members of the public prior to the quiz (call this set $P$), and they each have 100 seconds to name as many examples as they can (giving rise to a set $A_p\subseteq A_Q$ for each $p\in P$. The contestant gets a point for every one of the 100 people who named their answer $a$:

\[ \mbox{score}(a) = \begin{cases}
| \{p\in P : a\in A_p \} | & \mbox{if}\ a\in A_Q \\
100 & \mbox{if}\ a\not\in A_Q.
\end{cases} \]

So an obvious answer like Die Hard or France will score a lot of points, and an obscure answer like Striking Distance or Central African Republic will score fewer points. Points are bad (hence the title) so it’s better to dredge up an obscure answer than stick with something safe. However an incorrect answer like Avatar or Mexico scores the maximum 100 points. At the end of the round the contestant with the most points is eliminated.

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