Archive for October, 2011

Vegan chocolate tray bake topped with ganache

October 30th, 2011 No comments

Vegan chocolate tray bakeI 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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Writing the script for Spain v Scotland

October 11th, 2011 Comments off

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.

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Here is a knockout formula

October 11th, 2011 No comments

a = 2 (n – R)

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

FA Cup draw

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.

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