The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: A Modest Inheritance

Dear Uncle Colin, My six siblings and I have inherited a fortune of £$10^{10} + 10^{(10^2)} + \dots 10^{(10^{10})}$, to be divided evenly between us. However, we’re a very squabbly family, so we want to know how much money will be left over once it’s divided up. Can you help?

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A Challenge to the Mathematical Ninja

“I beg your pardon?!” yelled the Mathematical Ninja. The terribly well-dressed gentleman stood his ground. “I said, sensei, I would work $0.8^{10}$ out differently.” A sarcastic laugh. “This, I have to see!” “Well, $8^{10} = 2^{30}$, which is about $10^{9}$.” “About.” “Obviously, we can do better with the binomial: $2^{10}$

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Wrong, But Useful: Episode 68

In this month’s thrilling installment of Wrong, But Useful, we’re joined by @c_j_smith, who is Calvin Smith in real life. We discuss… Number of the Podcast: 5 Are Fish and Chip shop owners good at maths? Two maths puns and a maths joke Are there ‘popular’ books that ‘lead you

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Ask Uncle Colin: Consecutiveness

Dear Uncle Colin, Can there be two or more consecutive irrational numbers? - Between A Number And Consecutive… Huh? Hi, BANACH, and thanks for your message! We… have a problem here. When you’re dealing with integers, consecutive is really neatly defined: every number has a single successor, a number that’s

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Google’s Keypad

One of the many lovely things about Big MathsJam is that I’ve found My People - I’ve made several very dear friends there, introduced others to the circle, and get to stay in touch with other maths fans through the year. It’s golden. Adam Atkinson is one of those dear

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Ask Uncle Colin: A Trigonometric Puzzle

Dear Uncle Colin, I’m given that $0 \le x \lt 180^o$, and that $\cos(x) + \sin(x) = \frac{1}{2}$. I have to find $p$ and $q$ such that $\tan(x) = -\frac{p + \sqrt{q}}{3}$. Where do I even start? - Some Identity Needing Evaluation Hi, SINE, and thanks for your message! There

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The Dictionary of Mathematical Eponymy: The Fermat Cubic

So far in the Dictionary of Mathematical Eponymy, I’ve not picked anyone properly famous. I mean, if you’re a keen recreational mathematician, you’ll have heard of Collatz or Banach; a serious mathematician might know about Daubechies, and a chess enthusiast would conceivably have come across Elo. But everyone has heard

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Ask Uncle Colin: Powers and squares

Dear Uncle Colin, I’m told that $5\times 2^x + 1$ (with $x$ a non-negative integer) is a square number - how do I find $x$? - A Baffling Equation. Logs? Hi, ABEL, and thanks for your message! We’re looking for a square number - let’s call it $y^2$ - that’s

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A strange number base

Aaaages ago, @vingaints tweeted: This is pretty wild. It feels like what the Basis Representation Theorem is for Integers but for Rational Numbers. Hmm - trying to prove it now. Feels like a tough one. Need to work some examples! — Ving Aints (@vingAints) September 18, 2018 In

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Ask Uncle Colin: The Probability of Winning

Dear Uncle Colin, Suppose Team 1 beats Team 2 by a score of 10-7, and Team 2 beats Team 3 by a score of 10-4. How would we predict the score of a match between Team 1 and Team 3? - Make A Team Calculation Happen Hi, MATCH, and thanks

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