I will write here from time to time about things I feel strongly enough about. I am a professor of mathematics in London. Like my namesake in Richard Brautigan’s novel *The Hawkline Monster: A Gothic Western*, I like to count things:

I count a lot of things that there’s no need to count. Just because that’s the way I am. But I count all the things that need to be counted.

The tagline is the start of an abecedarian poem (one word beginning with each letter of the alphabet in turn) by JoAnne Growney. I love it and thank her for letting me use it here.

What’s on this blog? If you go to the contents page, you will find an annotated list of the posts, categorised in what I hope is a helpful way.

Other stuff, such as my publications, lecture notes, timetable, photographs taken on walks, etc. can be found on my personal web page.

I began the blog on 13 May 2009, as a practice run; I had been asked to take over the administration of another blog and wanted to make my first mistakes in private. Since then, it has helped me keep my sanity amid the crazy things that sometimes go on in academic life. (It is no coincidence that material for posting here lives in a directory called “rants” on my computer.)

In August 2010 my blog was in the top 50 mathematical blogs sponsored by Online PhD Programs; and Gaurav Tiwari did me the honour of making it his blog of the month for August 2011, on his Digital Notebook. JoAnne Growney has a paper in the *Journal of Humanistic Mathematics* entitled “Looking at Math Blogs”; mine is one of those she looks at.

I also feature as one of the London Mathematical Society’s research links, and in an interview on the MathBlogging site.

A little more information is in “About” expanded, and if you want to read the first chapter of my autobiography, it is here.

Recently, I moved my collection of quotes about mathematics here.

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Read your blog and this may be something you may have ideas about:

n players

k players per team

Each player must play “with” and “against” every other player at least once and an equal number of times using a minimal number of matches.

An easy example:

—

Players = 1, 2, 3, 4 (n = 4)

2 players per team (k = 2)

Matches:

1, 2 vs. 3, 4

1, 3 vs. 2, 4

1, 4 vs. 2, 3

After those 3 matches, all players played “with” and “against” each other once.

As simple as it gets.

—

The challenge that is causing me trouble:

Find an efficient method to generate the minimal number of matches for any n and k.

It sounded trivial at first…at first.

Perhaps I am slightly misunderstanding you, but in your example 1 plays with 2 once and against 2 twice. Do you mean that each player playes with each other player the same number

rof times, and each player plays against each other player the same numbersof times?There is quite a lot to be said about this and I will try to respond in detail when I am a bit less busy. Do you object if I quote your mail in my posting on this?

Hi Peter,

Here is a corrected description of the problem. I had a typo in my original description:

n players

k players per team

Each player must:

1) play “with” and “against” every other player at least once,

2) play “with” every other player an equal number of times,

3) play “against” every other player an equal number of times,

…using a minimal number of matches. (hence as few rounds as possible)

An easy example:

—

Players = 1, 2, 3, 4 (n = 4)

2 players per team (k = 2)

Matches:

1, 2 vs. 3, 4

1, 3 vs. 2, 4

1, 4 vs. 2, 3

After those 3 matches, all players played “with” each other once and “against” each other twice. [1), 2), 3) are satisfied.]

As simple as it gets.

—

Sure, you can quote me.

Thanks. See my post of today for the case

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