# September, 2019

## Revisiting Minesweeper

Many moons ago, I looked into the game theory of Minesweeper, and - in particular, what you should do in this situation: I think I got my probabilities wrong there, and want to put that right. If you want to work out the correct move (and associated probabilities), you should

## Ask Uncle Colin: A Parametric Integration

Dear Uncle Colin, I have the parametric equations $x = (t+1)^2$ and $y = \frac{1}{2}t^3 + 3$ and the lines $y = 16 - x$ and $x=1$. I need to find the area enclosed by the curve, these two lines and the $x$-axis, but my answer doesn’t agree with the

## Calculating $e^e$ and $e^{-\frac{1}{e}}$

"The Mathematical Ninja is currently on sabbatical. Leave a message after the tone... or else!" Oh dear! How are we going to figure out $e^e$ now? Let alone $e^{-\frac{1}{e}}$? We'll just have to roll up our sleeves and get our thinking hats on, that's all. OK, $e^e$ First of all,

## Wrong, But Useful: Episode 71

In the 71st episode of Wrong, But Useful, we’re joined by @nookiedv, who is Anouk de Vos in real life. We discuss: Number of the podcast: 1729, a fairly uninteresting number. Sums of cubes updates: 33 42 3 is also interesting as there are two solutions but it’s unknown if

## Ask Uncle Colin: Multiple solutions

Dear Uncle Colin, I just solved $2\cos^2(4x)=1$ between 0 and $2\pi$ and found four solutions: $\frac{1}{16}\pi$, $\frac{3}{16}\pi$, $\frac{5}{16}\pi$ and $\frac{7}{16}\pi$. The answer scheme says there are sixteen solutions! Where have I gone wrong? Have You Perhaps A Trig Identity Answer? Hi, HYPATIA, and thanks for your message! Looking at your

## A double tangent

A puzzle via @CmonMattTHINK (Matt Enlow): There is a line that is tangent to the curve y = x^4 - x^3 at two distinct points. What is its equation? (Can you find it without calculus?) #iteachmath #math #maths #mathchat #mathschat — Matt Enlow (@CmonMattTHINK) December 21, 2018 (I think we

## Ask Uncle Colin: A Pair Of Birds

Dear Uncle Colin, I have a little problem. You see, there’s this bird, A, in its nest at time $t=0$ - the nest is at $(20, -17)$ - and it travels with a velocity of $-6\bi + 7\bj$ (in the appropriate units). But there’s another bird, B, whose nest is

## Nonupling

My cunning plan, back last August, was sadly foiled: @christianp refused to rise to the bait. I'd written a post about finding the smallest number such that moving its final digit to the front of the number doubles its value. It turned out, to my surprise, to be 17 digits

## Ask Uncle Colin: Meeting Graphs

Dear Uncle Colin, I’m told that the graphs of the functions $f(x) = x^3 + (a+b)x^2 + 3x -4$ and $g(x) = (x-3)^3 + 1$ touch - and I need to express $a$ in terms of $b$. Can you help? - Can’t Understand Basic Introductory Calculus Hi, CUBIC, and thanks

## Dictionary of Mathematical Eponymy: Ivory’s Theorem

I… I… I… *Looks up Ito’s Lemma* *Reaches for bargepole, then doesn’t touch it.* I… I… I… Oh! It says here, there’s a thing called Ivory’s Theorem1! What is Ivory’s Theorem? Despite the main paper I could find about it calling it “the famous Ivory’s Theorem”, it was fairly tricky