Maths prize for 18 December: 12 billiard balls

You have 12 billiard (or snooker) balls, all the same except one which is slightly heavier – or it may be slightly lighter – than the rest.

You have scales which you can use to compare balls (or groups of balls) with each other.

How can you identify the odd ball by using the scales only three times?

The “12 billiard balls” puzzle: hint 1

The “12 billiard balls” puzzle: hint 2

The “12 billiard balls” puzzle: hint 3

The “12 billiard balls” puzzle: hint 4

Counting solutions to equations in number theory

Notes from a lecture (19 June 2014) by Richard Taylor, who worked with Andrew Wiles to prove Fermat’s last theorem.

Click here for notes on Taylor’s lecture (pdf) .

And here is an article by Taylor explaining some of his ideas to non-specialist readers.

What engineers do, and how they use maths

Thanks to Hasnaa Shaddad and Chris Wright for coming to CoLA on 12 November 2015 to run a session on “What engineers do, and how they use maths”, focusing on the Rayleigh-Plesset bubble equation.

Answers for FP1 homework for 17/11/15 on solving cubic equations

12 November 2015: “What engineers do, and how they use maths”

Maths prize: casting out nines

The first ever printed maths book, as far as we know, was the “Treviso Arithmetic”, printed in Treviso, near Venice, in Italy, in 1478. A printed edition of Euclid’s “Elements” came out soon after, in 1482. Unlike Euclid, where everything is proofs, the Treviso Arithmetic was a collection of practical ideas to do or check calculations.