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Prize crossnumber, Issue 10

Our original prize crossnumber is featured on pages 48 and 49 of Issue 10.

Rules

  • 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 2 February 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 14 March 2020.

Correction: Clue 13A has been corrected to “49A reversed” instead of “49D reversed”.
Correction: Clue 38D has been corrected to “33A less than 39D” instead of “33A less than 39A”.
Clarificiation: The triangle in 6D is a right-angled triangle.
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Dear Dirichlet, Issue 10

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

Dear Dirichlet,

Boy, am I in a world of woes! In the coming months, I have to go into surgery six times for a whole host of illnesses. To its credit, the hospital has allowed me to arrange my own schedule. In your doctoral opinion, which procedures should I undergo first?

— Under the weather, Cambridge

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On the cover: Islamic geometry

From the exquisite patterns of the Alhambra palace in Spain to a jigsaw puzzle on a rainy day, tessellations (tilings of the plane using shapes with no overlaps or gaps) are everywhere. They are sometimes used for practical reasons: providing durable and water-resistant surfaces, or for efficiencies of space (like hexagons in a honeycomb). And sometimes they are there for aesthetic reasons: tessellations are known to have been used in architecture since at least 4000BC when the Sumerians decorated walls with patterns of clay tiles. Continue reading

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Top Ten: issues of Chalkdust

This issue, Top Ten features the top ten issues of Chalkdust! Then vote here on the top ten pictures of scorpions for issue 11!

At 10, it’s the tenth most egg-cellent issue of Chalkdust: issue 06.
At 9, it’s issue 02, the difficult second issue.
At 8, it’s John Lennon’s latest avant garde composition: issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09. issue 09.
At 7, it’s Puff, the Magic Dragon Curves by Peter, issue 05 and Mary.
At 6, it’s the issue that will explain why the vote to put this issue in sixth place is unfair: issue 03.
At 5, it’s When I’m issue 04 by The Beatles.
At 4, it’s the only issue printed on A5 paper (which was a mistake, just like the minidisc): issue 01.
At 3, it’s You’re my number three issue of Chalkdust by S Club issue 07.

After a whole year at number 1, it’s the issue that’s finally been knocked down to number 2: issue 08.
Topping the pops this issue, it’s a new entry and a brand new release: issue 10.
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Page 3 model: Bees

If you model rabbits under ideal circumstances, you may find that the number of pairs of rabbits each month follows the Fibonacci sequence.

In this case, ‘ideal circumstances’ is a euphemism for nonsense, as your assumptions would include blatant untruths such as “rabbits mate once a month every month except their first month alive”, “a pair of rabbits gives birth to exactly one pair of rabbits per month”, and “the hutch is infinitely big (and hence Starsky is very squashed)”.

Fibonacci numbers, however, are not completely absent from nature. They accurately describe a vastly superior animal: the honeybee.

Male bees (drones) come from unfertilised eggs, and so they only have one parent — the queen.
Female bees (workers or queens) come from fertilised eggs and so have two parents — the current queen and a drone.

If you follow a drone’s family tree backwards, you will see that a drone has:

Family tree of honeybees

The number of ancestors of a male bee follows the Fibonacci sequence.

Who would’ve expected that?!

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How to make: tessellating shortbread

You will need

  • 4kg butter
  • 6kg flour
  • $(2+\varepsilon)$kg sugar
  • an oven that has been preheated to 220°C
  • a rolling pin
  • an oven tray
  • a cooling rack
  • a knife or cookie cutter

Instructions

  1. Combine 4kg butter, 6kg flour and 2kg sugar in a large bowl with your hands.
  2. Roll out the dough on a flat surface.
  3. Cut the dough into equally shaped quadrilaterals.
  4. Place quadrilaterals on the baking tray and bake for $0.1\dot6$ hours.
  5. Place quadrilaterals on the cooling rack, sprinkle with $\varepsilon$kg sugar, leave to cool, then tessellate and eat.