A sample text widget

Etiam pulvinar consectetur dolor sed malesuada. Ut convallis euismod dolor nec pretium. Nunc ut tristique massa.

Nam sodales mi vitae dolor ullamcorper et vulputate enim accumsan. Morbi orci magna, tincidunt vitae molestie nec, molestie at mi. Nulla nulla lorem, suscipit in posuere in, interdum non magna.

Recreational maths

I have been getting into the puzzles section at the tail end of The Guardian newspaper which I get each week. Last week it asked you to prove that there are infinitely many different pairs of numbers (a,b) for which a+b=ab.

This is easy to prove but I admit I had to work at it while wandering around the golf course yesterday before the straightforward way of thinking about the issue presented itself. It is a few years since I have tried these sorts of mathematical recreational problems and I am rusty – as a school kid I went in maths competitions organised around the UNSW magazine Parabola which introduced advanced math thinking to school students.  One problem that I agonised over for a day or so until I saw a clear solution was to prove that in any group of N people there are at least 2 people who have shaken hands with the same number of other people.  I had a particular affection for such mathematical recreations that involved simple to state problems that involved real insight.

I remember reading in a biography of John Von Neumann that prior to WW2 the Hungarians held mathematics competitions in the parks of Budapest.

I worry a bit about is that I am so rarely forced to think things through carefully these days. University work can become routine because, as you age, you tend to draw on long-held intellectual capital rather than really taxing your brain.  You might even be more efficient at solving problems by drawing on this capital but it does make you more machine-like.

Leave a Reply