[Mike L]

This is all a bit too difficult for my poor old brain. I haven't been able to come up with a solution, but I do have a comment on Dreams' solution:

Spoiler:

Dreams, you say that there are three coins in each bag. You end up by paying the miser one of the bags. But that implies that you are allowed to give the miser two good coins and one fake, without telling him which is the fake.

I read the original problem as saying that you can't pass a fake coin. You seem to be saying that it doesn't matter if the miser gets a fake, provided he also gets the two good coins to which he is entitled.

I guess that's fair enough. After all, the miser has the means to determine which is the fake.

A good solution. Well done.

And thanks to PDurrant for this interesting problem, even though I spent much too much time thinking about it.