Christmas puzzle #3: Colouring by numbers

Puzzle #3 in our 2020 Christmas puzzle series

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.

1. Overlay your solution to puzzle #2 which also consists of a 15×20 grid. Colour any square in the grid which you shaded in the nonogram midnight blue.
2. For each remaining 3-digit palindromic prime, colour the middle digit black, eg if you found 101 (horizontally or vertically) you would colour in only the 0.
3. Colour all remaining 2-, 3-, or 4-digit Catalan numbers green.
4. Colour all remaining perfect numbers with at least 2 digits brown.
5. Colour all remaining numbers which are prime numbers between 5 and 97 squared red.
6. Colour all remaining 3- or 5-digit star numbers (OEIS A003154) yellow.
7. Colour all remaining Leyland prime numbers with at least 2 digits grey.
8. Finally, colour all remaining 1-digit perfect numbers orange.

Leave all remaining squares white. The result is a charming mathematical winter scene, and the solution to this final puzzle.

The puzzle

We will post solutions to all three puzzles in a week. In the meantime why not let us know how you have got on via Twitter @chalkdustmag.

• Book of the Year 2020

We announce the winner of this coveted prize