The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: A Six-Digit Square

Dear Uncle Colin, I’m told a six-digit number, ABC,DEF1, is a perfect square such that DEF is 8 times ABC. How do I find this number? - Very Interesting, Except That Eight Hello, VIETE, and thanks for your message! This is as much of a typographical challenge as it is

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Tactical Voting

As a progressively more adamant Europhile, I was pleased to learn that the UK would take part in next month’s European Parliament elections1. As an amateur psephologist, I was delighted. Rather glibly, I responded to someone asking whether one needed to vote tactictally in these elections by saying “no, it’s

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Ask Uncle Colin: A round-robin

Dear Uncle Colin I’m organising a tournament with 16 teams, and wanted to arrange it in five stages, each consisting of four groups of four teams. However, I found that after three rounds, it wasn’t possible to find any groups without making teams play each other again! Why is that?

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Heads, Tails and Bumpsdaisy, revisited

At a recent East Dorset Mathsjam , the puzzle of two heads resurfaced: if you repeatedly flip a fair coin, how long (on average) do you have to wait until you get two heads in a row? Two fine answers are available here. However, the estimable Barney Maunder-Taylor went down

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Ask Uncle Colin: Disguised quadratics

Dear Uncle Colin, I have to solve $5^x = 6 - 5^{1-x}$ - I understand it’s going to end up as a quadratic, but I can’t see how! - Explain, Uncle Colin, Like I Demand! Hi, EUCLID and thanks for your message! The key thing here is to spot that

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The Dictionary of Mathematical Eponymy: Daubechies Wavelets

Before I dive in to Daubechies wavelets, a confession: at university, Fourier series were the bane of my existence. I could do them, under duress, but in the same way as I set up the audio for Wrong, But Useful1: I had a recipe of steps I needed to follow,

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Ask Uncle Colin: Traffic Flow

Dear Uncle Colin, I read that when cars are driving at 70mph on the motorway, they take up more space than when they travel more slowly (because you need to leave a longer safe gap between them). What’s the most efficient speed for motorway travel if you want to get

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The Mathematical Ninja and the Ninety-Sevenths

“A ninety-seventh.” The student scratched her head. “I’d call that 0.01.” A moment more’s thought. “0.0103? Probably good enough.” For the Mathematical Ninja, this was about as good as could be expected. They sighed all the same and wrote down: $0. \dot 01\, 03\, 09\, 27\, 83\, 50\, 51 \\

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Wrong, But Useful: Episode 65

In this month’s Wrong, But Useful, we’re joined by @televisionduck, who is TD Dang in real life. We discuss: Chalkdust Issue 091 Fun spring cover with Harris spiral, Horoscope is back!, New academic webpage checklist (c.f. Colin’s old webpage, @standupmaths interview, top ten regulars, etc. Write for them! Talkdust, second

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Ask Uncle Colin: A Fishy Derivative

Dear Uncle Colin, I have the equation of a curve, $\frac{2x+3y}{x^2 + y^2} = 9$. If I differentiate implicitly using the quotient rule, I get $\diff{y}{x} = \frac{2(x^2 + 3xy - y^2)}{3x^2 - 4xy - 3y^2}$. If I rearrange first to make it $2x + 3y = 9\left(x^2 + y^2\right)$,

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