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Christmas puzzle #3: Colouring by numbers

Happy Boxing day! That means it’s time for the third and final Chalkdust Christmas puzzle. We hope you have been enjoying them so far! You can find the first two puzzles here and here.

The rules

  • Below is a 15×20 grid and each square contains a digit 0–9. Your job is to colour in each of the squares according to the rules below.
  • If a square has already been coloured in as part of a previous rule, then it, together with the digit it contains, should be ignored—in other words you should apply the rules in the order they are given, and only to the remaining white squares.
  • Numbers clued by a given rule may overlap, so a digit can be part of several answers corresponding to the same colour.
  • Where a rule is of the form ‘Colour all numbers of type $x$ colour $y$’, the numbers will appear either horizontally left-to-right, or vertically top-to-bottom, never reversed or along diagonals.
  • None of the rules refer to numbers which start with a 0.
  • Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.

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Christmas puzzle #1: Christmas tree sudoku

Here at Chalkdust, we like to celebrate Christmas as much as the next magazine for the mathematically curious, and what better way to celebrate than with a few yuletide mathematical puzzles. We have three for you, the first one you can find below, the second one will be published tomorrow (Christmas Day), and the final one the day after (Boxing Day). They are the perfect accompaniment to an warming hot chocolate and mince pie. Each puzzle is related to the previous one, so keep a hold of your solutions ready for the next day. We hope you enjoy giving them a go and the whole team wishes you a very merry Christmas!

The rules

  • Normal sudoku rules apply: you must complete the 9×9 grid with the digits 1 to 9 such that each digit appears exactly once in each row, column, and 3×3 block.
  • The digits that appear on each thermometer must strictly increase as you move away from the bulb. The colours of the thermometers are purely decorative and do not affect the puzzle.
  • The digits on the baubles are all even.
  • The digits on the stars are all prime.

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Dear Dirichlet Christmas special

Dear Dirichlet

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

Dear Dirichlet,

My flatmates and I put up our square-shaped artificial Christmas tree last week and decorated it beautifully. However, when I get home from work, I find it on its side on the floor. I think my flatmates are pushing it over but it doesn’t matter how much I shout at them, they insist it’s not their fault. Do you know why this is happening?

— Tinselitus, Glasgow

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