The Apprentice - legal question

Factual Questions
1

On a recent episode of The Apprentice (UK version), the task was to design and sell a board game. Watching it, A legal question occurred to me. Who owns the rights to the design? If, hypothetically speaking, the game was successful, who could sell it? All bar one candidates will eventually be fired, could they then set up in business selling their game? Or would it be the property of the BBC, or Alan Sugar?

Same goes for any other of their tasks. Or, for that matter, the US version of the show, or any other countries that have it.

I wasn’t sure where to post this. It’s a factual question, about what the law is, more than a discussion of the show. And I’m not looking for legal advice. So I think GQ rather than CS or IMHO. I suppose the mods will move it if they disagree.

2

I have never been on the show, so I can’t say from experience, but it would surprise me if the contestants hadn’t signed away all rights to products, ideas, and anything else that had to do with what happens while they are contestants.

3

This was almost certainly covered in the contract that the contestants signed when they agreed to be on the show. Were it not covered, I assume that the game would be considered a “work for hire” under US law, and probably under the British equivalent as well.