Possible Clues:

• Puzzle
• Mental challenge
• Difficult puzzle
• Poser
• New meal introduced by one kind of cook is a puzzle
• Cups, among Darjeeling and Earl Grey, the Queen finds a problem
• Be struggling with a trainer's tricky problem
• "If three hens lay three eggs in three days ...," e.g.
• Puzzle requiring thought
• Puzzle touring Aintree bars