Browsing category ninja maths

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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The Mathematical Ninja and $\arctan(0.4)$

It took the Mathematical Ninja a little longer than normal; the student had managed to rummage around in her bag and lay a finger on the calculator before simultaneously feeling her arm pulled away by a lasso and hearing "0.3805. Or, as a one-off, since the question is asking for

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Powers

“Here’s a quick one,” suggested a fellow tutor. “Prove that $2^{50} < 3^{33}$.” Easy, I thought: but I knew better than to say it aloud. First approach “I know that $9 > 8$,” I said, checking on my fingers. “So if $2^3 < 3^2$, then $2^{150} < 3^{100}$ and $2^{50}

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The Mathematical Ninja and the Variable Volume

The student, at the third time of asking, navigated the perilous straits of negative powers and fractions of $\pi$ and came to rest, exhausted, on the answer: "$r^3 = \frac{500}{\pi}$," he said. The Mathematical Ninja stopped poking him with the foam sword (going soft? perhaps. Or perhaps this student needed

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The Mathematical Ninja and the Cube Root of 4

The student swam away, thinking almost as hard as he was swimming. The cube root of four? The square root was easy enough, he could do that in his sleep. But the cube root? OK. Breathe. It's between 1 and 2, obviously. What's 1.5 cubed? The Mathematical Ninja isn't going

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The Mathematical Ninja and the SSNs

A professor - according to Reddit - asked their class how many people you'd need to have in a room to be absolutely certain two of them would have Social Security numbers1 ending in the same four digits (in the same order). 10001, obviously. How about a probability of 99.9%?

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Using Units to Deal With Density

Glancing over sample papers for the new GCSE, I stumbled on this: Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy. Metal A has a density of $19.3 \unit{g/cm^3}$. Metal B has a density of $8.9 \unit{g/cm^3}$. Work out the density of

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The Mathematical Ninja and $\sin(15º)$

The Mathematical Ninja sniffed. "$4\sin(15º)$? Degrees? In my classroom?" "Uh uh sorry, sensei, I mean $4\sin\br{\piby{12}}$, obviously, I was just reading from the textmmmff." "Don't eat it all at once. Now, $4\sin\br{\piby{12}}$ is an interesting one. You know all about Ailes' Rectangle, of course, so you know that $\sin\br{\piby{12}}=\frac{\sqrt{6}-\sqrt{2}}{4}$, which

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The Maths Behind… Cakes

"Cooking," said my friend Liz in a recent Facebook post, "is one of the activities where maths is most useful in my everyday life." She added this picture: I've got several reasons for wanting to share this. 1. It's pretty much a model answer Imagine you're in a GCSE exam,

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Ask Uncle Colin: Shouldn’t this be simple?

Dear Uncle Colin, I've got a funny square and I can't find $x$. Can you help? - Oughta Be Simple, Can't Unravel Resulting Equations Hi, OBSCURE, and thanks for your message! You're right, it ought to be simple... but it turns out not to be. It is simple enough to

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