Rising chair by Robert van Embricqs:
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- a+b+c+d+e+f = y
- ab+cd+ef=10y
- abc+def=100y
- a+b+c+d+e+f = y
- 10a+b+10c+d+10e+f=10y
- 100a+10b+c+100d+10e+f=100y
Almost all above average
This morning James Grime tweeted about a BBC News article, “‘Third of UK postcodes’ have slow broadband speeds“. This quotes Julia Stent, director of telecoms at uSwitch saying:
Britain might be riding the wave of a super-fast broadband revolution, but for 49% who get less than the national average broadband speed, the wave isn’t causing so much a splash as a ripple.
Now, the thrust of the article, that broadband speeds are undesirably slow in some parts of the country, might be valid, but the appeal to the “average” is a very weak argument (Update [23:47]: Although, please see the comment below). The result that 49% are below average should not come as a big surprise!
James, rightly, questions which average is most appropriate, but I am more interested in a tweet by Ian Preston:
We can make almost everyone above average if we are happy for one person to be really badly off.
This, of course, is quite right.
Unless I’m reading it wrong (and I may well be), the Bank of England’s Lending to Individuals December 2011 has outstanding net lending to individuals as £1451.4 billion. The UK Office for National Statistics gives the Public Sector Net Debt excluding financial interventions as £988.7 billion (January 2012) and Total population (UK) as 62.3 million (mid-2010).
If we gave one person all that debt and everyone else zero, then a simple average would be £2.44 trillion divided by 62.3 million people, which is £39,167.
Since almost everyone is worth zero, we would almost all be 39 thousand pounds above average. Sound good? This would sort out Government debt and make almost all of us “above average”. And if we’re “above average” then, erm, everything is fine, right?
(Flaws in the argument left as an exercise for the reader!)
Newcastle MathsJam February 2012 Recap
February’s MathsJam was loads of fun! We had a record attendance of 14 cheery people who just about managed to fit around the biggest table in the Charles Grey.
After last month’s puzzlocalypse, which left me for over a week unable to count the toes on my feet, I wanted to have a nice relaxed evening.
Click here to continue reading Newcastle MathsJam February 2012 Recap on cp’s mathem-o-blog
Geo by Mika Barr for Talents Design
Geo by Mika Barr for Talents Design:
Barriers to teaching
Lecturer in Mathematics.
School of Mathematics, University of Excellence.
Competitive salary.
Applications are invited for the post of Lecturer in Mathematics.
The University of Excellence is ambitious for the future, priding itself on its commitment to world-leading research and investment in an outstanding research environment. The opportunity is available to join a dynamic, highly esteemed and international research programme. Candidates who can interact with one or more of the School’s existing research strengths are particularly encouraged to apply.
As a successful candidate, you will have a PhD (or equivalent) in some branch of Mathematics and a track record of relevant research. You will have demonstrated the ability to publish consistently in leading research journals and be able to provide evidence of your experience attracting research funding. You will advance the School’s research agenda by supervising a group of PhD researchers.
In the latest UK Research Assessment Exercise the School submitted research output from over 70 staff. 65% of this research was recognised as being either world-leading or internationally excellent in terms of originality, significance and rigour.
Underpinned by the quality of its research, the School offers a range of degrees from undergraduate to postgraduate level. The successful candidate will also be expected to contribute to the development and delivery of teaching in Mathematics.
Potential candidates are encouraged to check our website for full details.
Reading around the Alan Turing Pardon
I have a piece in this week’s Pod Delusion episode 123 at 45:00 on the pardon for Alan Turing.
Here are links to some of the bits I talked about in this.
I spoke about concerns of overdoing the Turing celebrations, saying: what Turing did was brilliant, but we should celebrate what Turing actually did, not some imagined feats, and we should not forget others in doing so. You can read more about this and find out about the article which suggested that had Turing lived then Silicon Valley might have been started in the UK at ‘Beware the Alan Turing fetish‘ by John Graham-Cumming.
Turing was convicted under Section 11 of the Criminal Law Amendment Act 1885. In 2009 Gordon Brown issued an official apology for the way Turing was treated. Read about the official Government apology in ‘PM’s apology to codebreaker Alan Turing: we were inhumane‘. Read how the apology came about in ‘How Alan Turing Finally Got a Posthumous Apology‘ by John Graham-Cumming.
Now there is a current e-petition calling for a pardon for Turing. John Leech MP issued an early day motion calling for this pardon. (I also mentioned the current e-petition calling for a pardon for Oscar Wilde.)
Asked a question in House of Lords, a Government Justice Minister said “a posthumous pardon was not considered appropriate”. Read the text of Lord McNally’s statement.
I’ve seen the refusal to pardon Turing described as “homophobic” and an “act of malice“. Particularly, the complaint is that Turing is still seen as a criminal in the eyes of the law.
John Graham-Cumming on ‘Why I’m not supporting the campaign for a pardon for Alan Turing‘, in which he writes about the Protection of Freedoms Bill, which “specifically allows for the disregarding of convictions under the old law that was used against Turing”.
To honour Turing I suggested you might attend events under the Alan Turing Year banner, or donate to Bletchley Park’s Action This Day! fundraising campaign.
This piece used audio from episodes 84 and 85 of the Pulse-Project Math/Maths Podcast.
A puzzle from James Grime about abcdef
Today James Grime tweeted this question/puzzle:
Is there a six digit number abcdef such that the following all hold?
If not, show why not.
A little tweeting back and forth verified that “ab” means 10a+b not a×b.
If you want to have a go at this, don’t read any further until you have!
First, rewrite the expressions so that both sides use standard arithmetic:
I noticed that since a, b, c, d, e and f are all positive integers, so must y be. Then 10y must end in 0 and 100y must end in 00.
From 3, we see that in 100y only c and f contribute to the units, so c+f=0, or f=-c. See also that only b and e contribute to the 10s, so b+e=, or e=-b.
Since a, b, c, d, e and f are positive digits 0-9, the only values that satisfy these equations are c=f=0 and b=e=0.
From 2, we see that in 10y only b, d and f contribute to the units. Therefore b+d+f=0, or d=b+f. Since b=f=0, we know that d=0.
So solutions to this problem have a being any digit 0-9, b=c=d=e=f=0, and so y=a.
The answer isn’t no, nor is it quite yes. These multiples of 100000 are not exactly interesting!
After I emailed Jim I was interested to see this solution, posted at The Wandering Monster, which took a substitution approach. On Twitter Dave Hughes gave his approach: “My solution was inelegant – I threw a C# program at it“. How interesting to see how different people approach a problem!
Update (20 mins after posting!): Please check the comments for a caveat I’ve missed.