"Toxin X is a substance that will make you violently ill for a few hours. However, it has no long term effects of any kind. As an experiment in psychology, I'm offering you a million dollars if tonight at midnight you fully intend to drink toxin X by tomorrow at noon. You don't actually have to drink the toxin; all you have to do is to intend to drink it. Your intention will be tested by a device similar to a polygraph which my people have developed and which has been shown to be 100% accurate. If at midnight you have the intention, a million will be wired to your bank account. The only other conditions are that you are to make no bets, do anything that will cause you to become irrational, or arrange for any way to avoid the effects of the toxin."

Suppose you decide that being ill for one day is a reasonable price to pay for a million dollars. Your first thought is to therefore agree to the proposal. It then occurs to you that you won't even have to become sick in order to win the money. All you have to do is to intend to drink the toxin. You don't actually have to carry out your intention.

But now if you know ahead of time that you don't actually have to drink the toxin, then you can't really intend to drink it. So you tell yourself you really do have to drink it. But then if at midnight you really did intend to drink the toxin, and you got the million, then come the next day you would no longer have any reason to drink it: you've already been paid and drinking the toxin would make you unnecessarily sick.

Is there any way for you to win the money?

I'm not sure that knowing that ten men will force you to drink the toxin, no matter how much you kick and scream, really counts as you 'intending' to drink it.

Using the ten men in a slightly different way, however, I think it can work. Arrange it so that, right after receiving the money, you will have the million taken from you by the ten men. The ten men will then only give you the money if you drink the toxin in front of them. Since you know that this is what is going to happen before hand, you know full well that you plan on drinking the toxin (or you won't get the money). Therefore you really will intend to drink the toxin when given the polygraph test.