My daughter loves to draw and doodle. She has the artistic gift, something that passed me by. She doodled this simple little portrait of me the other day and I was impressed how she had captured something about me, even though it’s a very simple sketch.
Here it is morphing out of the real thing. What do you think?

This has been a staple favourite of mine if I’m entertaining as it works well as a party buffet snack (chopped in quarters) or as part of a main meal served with rice and salad. These are dead easy (a food processor is required) to prepare and turn out extremely tasty.
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I went along to my first meetup of the Edinburgh Cinema group and Elise the facilitator had generously baked a chocolate cake for everyone. This was my first knowing encounter with ganache as an icing alternative and I was pointed towards Beatty’s Chocolate Cake for the recipe of the deliciously moist cake.
Inspired by this, I fancied adapting this into a vegan tray-bake and my first attempt turned out no’ too bad.
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Even if, like me, you’re not a Scot, you probably still feel a sense of a pre-ordained script for tonight’s Euro 2012 qualifier in Alicante. Scotland have that traditional glimmer of a chance at making it to the next stage. It is even in their hands – beat Spain and they are through to the play-offs.
But Scottish sport doesn’t usually work like that. The script generally goes like this:
The small glimmer of hope is consolidated by valiant and sometimes heroic efforts.
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…
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