Prize crossnumber, Issue 09

Our original prize crossnumber is featured on pages 54 and 55 of Issue 09.


  • Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Word DVD, a dodecaplex puzzle and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. The prizes have been provided by Maths Gear, a website that sells nerdy things worldwide. Find out more at
  • To enter, submit the sum of the across clues via this form by 9 September 2019. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 28 September 2019.

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Dear Dirichlet, Issue 09

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to

Dear Dirichlet,

My husband and I have found ourselves in a long-distance relationship. His company offered him a large promotion if he moved to Canada for six months, but it seems now that the position will require more time. I’m not sure that I want to move out there with him, or that I could be happy knowing he had to move back here. Conversation with the time difference is hard as well. Any tips?

— Getting tensor, Four Oaks

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Horoscope, Issue 09

Mar 21 – Apr 19

Your research output doesn’t look so bright until a tall, dark, handsome stranger presents you with a proof of the Riemann hypothesis.
Apr 20 – May 20

The heavens are not in your favour, and people may try to take advantage of you. Don’t let them take you for a mug.
May 21 – Jun 20

Tomorrow you will wake up in a parallel universe which is identical to this one, except for the fact that no one ever invented the Banach–Tarski paradox. So you get to invent it! Good for you!

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Top Ten: Chalkdust regulars

This issue, Top Ten features the top ten Chalkdust regulars! Then vote here on the top ten issues of Chalkdust for issue 10!

At 10, it’s the page you probably didn’t use to find this page: the contents page.
At 9, it’s the big block of text on the page that no-one looks at: the editorial.
Did you know that the online vote is the reason that did you know made it to number 8?
At 7, but about to move to 14 as an infinite number of people have arrived, it’s Hilbert’s hotel: the game.
At 6, it’s the puzzles page. Can you work out why it’s so popular?
At 5, and causing a moderate amount of recursion, it’s top ten.
At 4, despite being deemed not hot, it’s what’s hot and what’s not.
Storming back into the top ten after not being seen since issue 03, it’s the horoscope.

Dear Dirichlet,

what is the second most popular Chalkdust regular?

Dirichlet says: No idea.

Topping the pops this issue, it’s the crossnumber.

Page 3 model: Game of Thrones

Be warned: this article is dark and full of spoilers.

One of the best parts of getting into a series is getting to know and love the main characters. However, in Game of Thrones (or A Song of Ice and Fire, for you purists), this can be a heart-breaking activity. Who will survive to the end and who will bite the dust? No one knows, but perhaps maths can lend a hand.

Image: Andrew Beveridge

Andrew Beveridge and Jie Shan used network theory to investigate who the main characters of Game of Thrones are. The diagram above shows all the interactions between characters during the seventh series: the larger characters are more central, as determined by the PageRank algorithm.

However, it only takes one swing of an axe to drastically change the network…