a = 2 (n – R)

I always like a good real-world application of mathematics, in this case algebra.

Photo by Matlock

The question

If you’re organising a knockout tournament for something and the number of players or teams is not a neat power of two, how many players have to be drawn in round 1, so that round 2 is a neat power of two? I figured this out by solving this pair of equations:

a + b = n
0.5a + b = R

where a is the number of players to be drawn in round 1, b is the remainder of players to be drawn in round 2, n is the total no. of players and R is the largest power of two less than or equal to n.

Solving the equations

0.5a + (n-a) = R
a + 2n - 2a = 2R
2n - a = 2R
a = 2n - 2R
a = 2(n - R)

An example

91 players enter our tournament, how many must be drawn in round 1?
n = 91, R = 64
a = 2 x (91 - 64)
a = 54
So we draw 54 players in round 1, which produces 27 winners to meet the remaining 37 players in round 2.

I have repeated the sampling of Twitter’s “sprinkler hose” that I carried out in April 2010. The data suggests that less than 10% of Twitter users are using twitter.com to interact with Twitter. The sample is based on 116,293 tweets captured between 4pm and 5pm BST on 11 Sep 2011. Read more…

Following my experiment with sampling the public Twitter timeline this morning, I ran another sample, this time for much longer and at a time of day, when many American users would be active to get a slightly more accurate breakdown of the top twenty Twitter clients. Read more…

This is an appendix to my post on Sampling Twitter to determine client breakdown. Below is the full breakdown of the client source of tweets sampled on 14 April 2010 for around 15 minutes from 12.30pm UK time. Total tweets sampled: 21912. Read more…

The arrival of promoted tweets on Twitter got me thinking about how people post their tweets, as the initial dipping of the Twitter toe into monetization will only impact users of http://search.twitter.com.

So, how many people actually use the Twitter.com website to post their tweets? What are the most popular clients? Read more…

…but the workaround is even worse

I’ve been a relatively happy user of Windows Live Mail since I started using it 18 months ago or so. But Microsoft gave me no option recently but to upgrade to the latest version of Windows Live Mail when I decided to install Windows Live Messenger and the current colour scheme is shockingly awful and what is worse there are no options within the application to set up a user-defined colour scheme.

The main problem is that on your list of messages, Windows Live Mail now displays the subject text of read messages in an insipid barely legible gray colour. I googled the issue and found that there is indeed a solution, though I suspect there never was a more appropriate case for using the term workaround as the fix is arguably much more annoying than the Windows Live Mail problem it addresses. Read more…