Locking products using a question

I am looking to build a Woo-Commerce store for a client.
Each product is actually going to be a prize draw. Every purchase is a ticket for the draw.
To be able to enter the prize draw the visitor needs to answer a multiple choice question.
So I need to be able to lock each product so that they can only be sold once the user has answered a question.
Are there any ideas as to how I could implement that, or any plugins that you know of that have that functionality?
Thanks
Sam