The solutions to the imp and pixie puzzles are below.
Happy Boxing Day!
A final post, to provide the solution to Friday’s puzzle.
Thanks for following the Indisputable Santa Mathematical Advent Calendar. Just a few loose ends to wrap up, with a solution to our Christmas Eve puzzle today, with the solution to Friday’s puzzle (Santa’s Dressing Room Disasters) to come tomorrow…
The not-so-fabulous mystery prize will be revealed tomorrow. The image is a clue to its identity.
UPDATE: The mystery prize is now revealed at the bottom of the solution page.
It turns out that my intuition was correct (the tiling is possible if and only if r is a rational number lying in the half open interval (0,1]), but the proof is not obvious. The maths involved seems to be rather lovely though, so Stephen’s comments are well worth a look.
As I mentioned previously, I think this is a good puzzle for mathematics learners at GCSE level or for those setting out on A-level courses, both for checking up on basic algebraic understanding and for illustrating some specific problem-solving skills. I have summarised the key learning points that I think the puzzle raises on the solution page.
Thanks to everyone who engaged with the Mad Hatter puzzle. The solution is now available. There is a link at the bottom of the puzzle page:
#3: Kidnapped by the Mad Hatter
A coloured hat puzzle!
Maths knowledge required: None
And HERE is a direct link to the solution.