Launch day puzzle hunt

The day is finally here: issue 11 is out now! To help you celebrate launch day in style, we’ve set a puzzle hunt: throughout the day, we are posting a series of puzzles. The answers to these puzzles form clues to the four-digit code for the door to let you into the Chalkdust issue 11 secret backstage lounge.

There are five puzzles in the puzzle hunt. They are being posted every 2 hours: at 9am, 11am, 1pm, 3pm and 5pm.


Prize crossnumber, Issue 11

Our original prize crossnumber is featured on pages 56 and 57 of Issue 11.


  • 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 Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
  • To enter, enter the sum of the across clues below by 3 September 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 October 2020.

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Dear Dirichlet, Issue 11

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

Dear Dirichlet,

You’ll be pleased to hear I’ve just finished my PhD in abstract algebra, but now I’m stressed about jobs. I need to write this grant application for a big postdoc position studying a set combined with two binary operations, but all I want to do is curl up and read my favourite book: JRR Tolkein’s The Two Towers. What should I do?

— Elven Safety, Birmingham

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Top ten vote issue 11

Which is the best maths-themed day out?

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Page 3 model: Cooking spaghetti

You there! Yes—you cooking the spaghetti! How do you tell when it’s cooked? No, don’t throw it against the wall… maths is here for you.

Cooking pasta increases the amount of water it contains until the pasta is fully hydrated, at which point we say it’s cooked. But this means that the pasta is no longer a rigid material—it’s flexible.

Nathaniel Goldberg and Oliver O’Reilly, in their 2020 paper, model the process of spaghetti cooking in a saucepan:

Measure the arclength, $s$, of your spaghetto from $s=0$ to $s=L$ and call the angle to the horizontal at any point $\theta(s)$:

Flexible rod theory tells you that the moment along the spaghetto, $\boldsymbol{m}$, depends on the angle, $\theta$, and the weight force, $\boldsymbol{n}$. For a bent spaghetto, you can write the curvature, $\kappa$, in terms of the intrinsic curvature, $\kappa_0$, and the moment, divided by the rigidity, $EI$: \[\frac{\partial\theta}{\partial s} = \kappa = \kappa_0 + \frac{m}{EI}.\]

In the pan!

But the intrinsic curvature changes as water is absorbed. Goldberg & O’Reilly use a model from plant stem growth for the rate of intrinsic curvature change, making it dependent on the amount of time the spaghetto has been in the water for:

\[\frac{\partial \kappa_0}{\partial t} = \alpha(t)(\kappa – \kappa_0) \quad \text{where} \quad \alpha(t) = \alpha_{\infty}\frac{1-\mathrm{e}^{-t/\tau}}{1+\mathrm{e}^{-(t-t_0)/\tau}}.\]

Want the spaghetti al dente? Better get working out the parameters $\alpha_\infty$ and $\tau$…


  1. NN Goldbery & OM O’Reilly Mechanics-based model for the cooking-induced deformation of spaghetti, Physical Review E, 101, 03001, (2020).

Top Ten: pictures of scorpions

This issue, Top Ten features the top ten pictures of scorpions! Then vote here on the top ten maths-themed days out for issue 12!

At 10, it’s Wind of Change by The Scorpions.
At 9, it’s scorPioneers by Bloc Party.
At 8, it’s scorpIonisation, Edgard Var&egrace;se’s work that features only percussion instruments.
At 7, it’s scorpiOne by U2.
At 6, it’s sCorpus Christi Carol by Jeff Buckley.
At 5, it’s scorpiOnce in a Lifetime by The Talking Heads.
At 4, it’s scorpiOn The Road Again by Willie Nelson.
At 3, it’s scorpiOne of These Days by Camper Van Beethoven.

At 2, it’s I Write Sins Not Tragedies by Panic! at the Discorpion.
Topping the pops this issue, it’s the album Scorpion by Drake.