# Browsing category puzzles

## Constructing the square root of 6

On Twitter, @RuedigerSimpson pointed me at an episode of My Favourite Theorem in which @FawnPNguyen mentioned a method for constructing $\sqrt{7}$: draw a circle of radius 4 construct a perpendicular to the radius at a distance of 3 from the centre the distance between the base of the perpendicular and

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## A Harmonic Conundrum

This one came from user_1312 on reddit with a heading “This is a bit tricky… Enjoy!”. What else can we do but solve it? Let $m$ and $n$ be positive numbers such that $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{101}$. Prove that $m-n$ is a multiple

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## Summing Products

Some days your mind wanders into an interesting puzzle: not necessarily because it’s a difficult puzzle, but because it has familiar result. Then the puzzle becomes, how are the two things linked? For example, I had cause to add up all of the numbers in the times tables - let’s

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## A folding puzzle

Here’s a tweet from @colinthemathmo: Here's another one. Take a square, crease in the halfway mark, fold up a corner - where does the corner go to? What are its coordinates? pic.twitter.com/Bfr0X8ACur — Colin Wright (@ColinTheMathmo) February 12, 2018 I’m not big on origami, but if Colin thinks it’s an

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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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## 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?

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## 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

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## A Puzzle From The MathsJam Shout (With Generating Functions)

In a recent MathsJam Shout, courtesy of Bristol MathsJam, we were given a situation, which I paraphrase: Cards bearing the letters A to E are shuffled and placed face-down on the table. You predict which of the cards bears which letter (You make all of your guesses before anything is

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## On Epiphanies

I had a fascinating conversation on Twitter the other day about, I suppose, different modes of solving a problem. Here’s where it started: Heh. You spend half an hour knee-deep in STEP algebra, solve it, then realise that tweaking the diagram a tiny bit turns it into a two-liner. —

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## A tasty puzzle

Normally when I call something a tasty puzzle, it's a lame local-paper pun about it being to do with cakes or something. In this case, it's not even that. Sorry to disappoint. Instead, it's a puzzle that came to me via reddit: Find $\sum_{i=1}^{10} \frac{2}{4^{\frac{i}{11}}+2}$. Eleventh roots? That's likely to

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##### Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.