# Browsing category big in finland

## Ask Uncle Colin: A Missing Digit

Dear Uncle Colin, A seven-digit integer has 870,720 as its last six digits. It is the product of six consecutive even integers. What is the missing first digit? Please Reveal Our Digit! Underlying Calculation Too Hi, PRODUCT, and thanks for your message! There are several approaches to this (as usual)

## A coin sequence conundrum

Zeke and Monty play a game. They repeatedly toss a coin until either the sequence tail-tail-head (TTH) or the sequence tail-head-head (THH) appears. If TTH shows up first, Zeke wins; if THH shows up first, Monty wins. What is the probability that Zeke wins? My first reaction to this question

## An alternative proof of the $\sin(2x)$ identity

Uncle Colin recently explained how he would prove the identity $\sin(2x) \equiv 2 \sin(x)\cos(x)$. Naturally, that isn't the only proof. @traumath pointed me at an especially elegant one involving the unit circle. Suppose we have an isosceles triangle set up like this: The vertical 'base' of the triangle is $2\sin(\alpha)$

## Review: Things To Make And Do In The Fourth Dimension, by Matt Parker

It's genuinely difficult to write an innovative maths book, something that'll teach even the most grizzled and cynical of tutors a thing or two, but @standupmaths1 has done exactly that. Most popular maths books, my own included, tread a pretty familiar path through the history of maths, throw out a

## A tennis puzzle

A puzzle that occurred to me watching Wimbledon this week: A tennis match goes to five sets. The number of games one of the players wins in each set forms an arithmetic series. Given that the two players won the same number of games in total, who won the match?

## Ask Uncle Colin: Is the Fibonacci series witchcraft?

Dear Uncle Colin, I read somewhere that if you work out $\frac{1}{999,999,999,998,999,999,999,999}$, you get the Fibonacci sequence. Is that really true? Is there witchcraft at work? -- Feeling Inspired By Ordinary Numbers; Arithmetic Calculation Can Intimidate! Hi, FIBONACCI! First, to put your mind at rest, there's no witchcraft at work

## A circle problem that succumbs to a circle theorem

A tweet from @GregSchwanbeck some time back asked: Does square or circle have greater perimeter? A surprisingly hard prob for HS: http://t.co/vwLIs26pcC #mathchat #math pic.twitter.com/Vpjop8yU7G — Greg Schwanbeck (@GregSchwanbeck) March 16, 2015 The setup is: one side of a square is tangent to a circle, and two corners of the

## The Mathematical Pirate’s Guide to Factorising Cubics

“Yarr,” said the Mathematical Pirate. “Ye’ll have plundered a decent calculator, of course?” “Er… well, I bought it from Argos, but… aye, cap’n! A Casio fx-83 GT PLUS!” “A fine calculator,” said the Mathematical Pirate. “One that offers you at least three ways to factorise cubics.” “Really!? I thought you

## Arccosine: secrets of the Mathematical Ninja

“$\cos^{-1}(0.93333)$, said the student. A GCSE student, struggling a little; the Mathematical Ninja bit his tongue rather than correct him to $\arccos$ or to $\frac {14}{15}$; he also accepted, grudgingly, the answer was going to be in degrees. “Maybe 21 bad degrees?” “21.04”, said the student. “Not too terrible.” “I

## How The Mathematical Ninja Divides By 49

"... which works out to be $\frac{13}{49}$," said the student, carefully avoiding any calculator use. "Which is $0.265306122...$", said the Mathematical Ninja, with the briefest of pauses after the 5. "I presume you could go on?" "$...448979591...$" "All right, all right, all right. I suppose you're going to tell me