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.
The solution to the Ultimate Tiebreaker puzzle is now available.
I have posted the solution for The Pirate Puzzle. After writing it, I discovered that the puzzle is actually a well-established part of the recreational mathematics canon, a fact that I had not been aware of. However, there are some important differences between my formulation and the way that the puzzle is generally stated, as I discuss at the end of the solution page.