# May, 2019

## 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

## 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! https://t.co/tgcy8iaXHa pic.twitter.com/tgcy8iaXHa — Ving Aints (@vingAints) September 18, 2018 In

## 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

## Cards and lattices

“That looks straightforward,” I thought. “I’ll keep on looking at this geometry puzzle.” Nut-uh. A standard pack of 52 cards is shuffled. The cards are turned over one at a time, and you guess whether each will be red or black. How many correct guesses do you expect to make?

## Wrong, But Useful: Episode 67

In this month's Wrong, But Useful, we're joined by @sheena2907, who is Sheena in real life. We discuss: Sheena's Number of the Podcast: 3,212 Board Games - Number Fluxx, Prime Climb Magic: The Gathering is undecidable! Oxbridge Time surprises The oddness of the Fibonacci sequence The heights of women Big

## Ask Uncle Colin: a fractional power

Dear Uncle Colin, How would you work out $\br{\frac{4}{5}}^{10}$ in your head? - Probability Estimation Needed, Relic Of Slide-rule Era Hi, PENROSE, and thanks for your message! That’s really two questions: how I would do it, and how the Mathematical Ninja would do it. Me Me, I’d probably use the

## A triangle puzzle

Like everyone else on Twitter, I’m a sucker for a nice-looking question, and @cshearer41 is a reliable source of such things. I particularly liked this one: There are two equilateral triangles inside this semicircle. What’s the area of the larger one? pic.twitter.com/Nvy01z2j5f — Catriona Shearer (@Cshearer41) November 7, 2018 Straight

## Ask Uncle Colin: an irrational power

Dear Uncle Colin, How would you work out something like $(-1)^\pi$? Doesn’t Everyone Miss Out Irrational Values Reckoning Exponents? Hi, DEMOIVRE, and thanks for your message! In the words of the politician: difficult, difficult, lemon difficult. One the one hand there is one answer that seems sensible - but on

## Dictionary of Mathematical Eponymy: Elo ratings

As I write this, classical chess’s top two players are Magnus Carlsen of Norway (rated 2835) and the USA’s Fabiano Caruana, who has a rating of 2832. Very close! But what do the rankings mean? FIDE1 uses the Elo rating system, a methodical - and mathematical - system for distilling

Dear Uncle Colin, In a culture where people have children until they have a daughter and then stop, what proportion will be daughters? * Families Retain Extra Girls Evidently Hi, FREGE, and thanks for your message1 ! Spoiler alert: it’s a half. There are several ways to see this, and