I imagine the following setup.
There is a contestant who has to pick one of three doors. How many prizes will be hidden is determined at random in the following way. Monty will toss a fair coin and if it comes up heads 2 prizes will be hidden behind the 3 doors, whilst if it comes up tails only 1 prize will be hidden. The contestant is informed about the rules, but Monty will not reveal any information to the contestant regarding the outcome of the toss.
The contestant now picks a door, and the game only continues if there is a prize behind it. However in order to win the prize the contestant will have to tell Monty what he thinks the result of the toss was ! If he s wrong he will not win anything.
The Question is what should the contestant answer, and does it matter what is answer is ? (naturally it is assumed he wants to win the prize)