This year has been frankly ridiculous. And while we’ve done our best to cover all the hot maths topics throughout, we have inevitably missed a few. Here’s some mathematical news bits and bobs from 2016 which we (and you!) may have not noticed.

# Relatively Prime is back!

Aperiodipal numero uno Samuel Hansen’s acclaimed podcast series *Relatively Prime* is back, on a new monthly schedule, with an episode about how PhD student Ibrahim Sharif designed a lottery to award licences to sell cannabis in the state of Washington.

When the stakes are so high (*geddit?! – Ed.*) you have to be really sure that your lottery is fair. That’s where a lot of fun maths comes in.

You can listen to *Lottery Daze* on relprime.com. Sam intends to fund this new incarnation of *Relatively Prime* through Patreon – you can pledge to pay Sam a certain amount (starting at a dollar) for every episode he releases, with perks for paying more such as a postcard from Sam or placing an ad in one of the episodes.

**Listen** to Lottery Daze on relprime.com

**Support** Relatively Prime on Patreon

# Mobile Numbers: Multiples of nine

*In this series of posts, Katie investigates simple mathematical concepts using the Google Sheets spreadsheet app on her phone. If you have a simple maths trick, pattern or concept you’d like to see illustrated in this series, please get in touch.*

We’re all (hopefully) aware that a pleasing property of numbers that are divisible by nine is that the sum of their digits is also divisible by nine.

It’s actually more well known that this works with multiples of three, and an even more pleasing fact is that the reason three and nine work is because nine is one less than the number base (10), and anything that’s a factor of this will also work – so, in base 13, this should work for multiples of 12, 6, 4, 3 and 2. Proving this is a bit of fun.

Once when I was thinking about this fact, an interesting secondary question occurred.

# Puzzlebomb – December 2016

Puzzlebomb is a monthly puzzle compendium. Issue 60 of Puzzlebomb, for December 2016, can be found here:

Puzzlebomb – Issue 60 – December 2016 (printer-friendly version)

The solutions to Issue 59 will be posted around one month from now.

This will be the last regular monthly Puzzlebomb – in future, there will be occasional one-offs but regular editions are taking a break. If you have any ideas for puzzles, please send them in! Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.

# Association for Women in Maths essay contest

The Association for Women in Mathematics in the USA is running its annual essay contest again, open to students in three age categories from Grade 6 to undergraduate.

Here’s the blurb:

To increase awareness of women’s ongoing contributions to the mathematical sciences, the Association for Women in Mathematics (AWM) and Math for America are co-sponsoring an essay contest for biographies of contemporary women mathematicians and statisticians in academic, industrial, and government careers.

The essays will be based primarily on an interview with a woman currently working in a mathematical sciences career. This contest is open to students in the following categories: Grades 6-8, Grades 9-12, and College Undergraduate. At least one winning submission will be chosen from each category. Winners will receive a prize, and their essays will be published online at the AWM web site. Additionally, a grand prize winner will have his or her submission published in the AWM Newsletter.

The deadline for entries is January the 31^{st} 2017, and if you want the AWM to pair you up with an interviewee, you need to get a request in by January 10^{th}.

All the prize-winning essays from previous years are online, including this nice one about Tanya Khovanova by high school student Emily Jia.

### More information

# CP’s solid used as the basis of a puzzle

Back in 2013, our own Christian Lawson-Perfect came up with a way of making a solid from the smallest non-Hamiltonian graph, the Herschel Graph. Called the Herschel Enneahedron, it’s got nine faces (three squares and six kites) and the same symmetries as the graph itself.

The most recent news is that Spektrum magazine – sort of a German version of New Scientist – has included in its regular puzzle column a Herschel Enneahedron-related challenge. Here’s Google’s best effort at translating it:

Please make a polyhedron of 3 squares and 6 cover-like kite rectangles with suitable dimensions (in your thoughts, drawings or with carton). What symmetry properties does it have, how many corners and edges? Is it possible to make a (Hamilton-) circular path on its edges, which takes each corner exactly once and does not use an edge more than once?

Before you get out your cartons and start working on this, given that we started from a graph which isn’t Hamiltonian, you may have a slight spoiler on the answer here… but the solution given includes some nice videos and explanation as to how the solid is formed.

# MathsBombe and Alan Turing Cryptography Competitions 2017 – registration open

Registration for the 2017 **Alan Turing Cryptography Competition** is now open!