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From the Mailbag: Golfing Combinatorics

Sam’s dad is in a mathematical conundrum – so she’s asked Katie, one of our editors, if maths can save the day.

From the Sartorial Arts Journal, New York, 1901Dear The Aperiodical,

My dad is going away on a golfing holiday with seven of his friends and, since I know a little bit about mathematics, he’s asked me to help him work out the best way to arrange the teams for the week. I’ve tried to work out a solution, but can’t seem to find one that fits.

They’ll be playing 5 games during the week, on 5 different days, and they’d like to split the group of 8 people into two teams of four each day. The problem is, they’d each like to play with each of their friends roughly the same amount – so each golfer should be on the same team as each other golfer at least twice, but no more than three times.

Can you help me figure it out?

Sam Coates, Manchester

‘All that glitters is not golden’: a Fibonacci Day Roundup

Golden ratio cake, from was 23/11, also known in some parts as 11/23, and you may recognise this as being a date made of the first four Fibonacci numbers. (Such numerical date-based Fibonacci coincidences haven’t been as exciting since 5/8/13, but at least this is one we can celebrate annually.) This meant that mathematicians everywhere got excited about #FibonacciDay, and spent the day talking about the amazing sequence. Here’s a round-up of some of the best bits, so you can celebrate Fibonacci day in style.

Matt Parker talks percentages

If anyone caught BBC1’s consumer moanfest Watchdog this week, they may have been pleasantly surprised to see Aperiodicobber Matt Parker featured in the show. Following a segment about a UK sports chain and its shocking use of the classic ‘UP TO 70% OFF’ ruse, they invited Matt on the show to explain how to calculate percentages more easily, and so that Anne Robinson could mock him for being Australian, apparently.

Since the tips Matt presented were useful, we at the Aperiodical thought it was worth reproducing Parker’s Patented Percentage Ploys here, for your reference.

How to solve a Rubik’s Cube in one easy step

Note: If you’re looking for instructions on solving Rubik’s cube from any position, there’s a good page at Think Maths.

One day some years ago I was sat at my desk idly toying with the office Rubik’s cube. Not attempting to solve it, I was just doing the same moves again and again. Particularly I was rotating one face a quarter-turn then rotating the whole cube by an orthogonal quarter-turn like this:

Having started with a solved cube, I knew eventually if I kept doing the same thing the cube would solve itself. But this didn’t seem to be happening – and I’d been doing this for some time by now. This seemed worthy of proper investigation.

3.142: a π round-up

Pi pie by Robert Couse-Baker. Photo used under the CC-BY 2.0 license.

π pie by Robert Couse-Baker. Photo used under the CC-BY 2.0 licence.

‘Tis the season to celebrate the circle constant! Yes, that’s right: in some calendar systems using some date notation, the day and month coincide with the first three digits of π, and mathematicians all over the world are celebrating with thematic baked goods and the wearing of irrational t-shirts.

And the internet’s maths cohort isn’t far behind. Here’s a round-up (geddit – round?!) of some of our favourites. In case you were wondering, we at The Aperiodical hadn’t forgotten about π day – we’re just saving ourselves for next year, when we’ll celebrate the magnificent “3.14.15”, which will for once be more accurate to the value of π than π approximation day on 22/7. (Admittedly, for the last few years, 3.14.14 and so on have strictly been closer to π than 22/7. But this will be the first time you can include the year and feel like you’re doing it right.)