# 3 cup trick in Magnificent Seven

I watched the Magnificent Seven the other night. In one scene one of the actors quickly shows how to turn 3 cups upright. It happened so quick that I wasn’t watching closely and think he cheated.

3 cups all upside down. He turns two over at a time. After 3 or 4 moves of turning 2 over at a time…all 3 are right side up.

I don’t think this can be done, but I haven’t given it rigorous thought. I think he cheated and in reality one of the cups was already right side up when he started (but before anyone noticed…it was a quick scene).

Two questions. Can someone take 3 upside down cups and turn two over at a time to get them all upright in 3-4 moves?

If you have the movie can you confirm that when he first does this, he cheated?

You can never get them all upright turning two over at a time. If you keep turning them over two at a time, you will make, in total, an even number of cup-turns. But to get them all upright, you need to turn each cup an odd number of total times, meaning the total number of cup-turns you make will be a sum of three odd numbers, which will be odd.

I’ve never seen the movie but this is the common bar bet:

Set up three glasses on the bartop, two pointing up and one pointing down. Your opponent is allowed three turns and with each turn he must flip two glasses. It’s impossible if the three glasses are initially placed 2 up, 1 down.

After your opponent gives up, “reset” the glasses but set them up as 2 down, 1 up. Following the same rules, you will be able to end up with all three glasses pointing up in three turns.

I’m confused. You can get it in one turn. Just flip the two down cups up. All three are pointing up now. Or do you mean exactly in three turns? Cuz then you just flip any two down and up again. Am I missing a rule?

Read it more carefully. There’s only 1 down cup in the unwinnable scenario*; the two down cups are in the winnable scenario. The idea is that you make the bar bet with the intention to cheat by initially setting it up in the unwinnable scenario for your opponent, and then sneakily “resetting” it into the distinct winnable scenario for your own turn.

*: For the reasons I outlined above, if you start with an odd number of down cups, you can’t win, ever. (While, of course, obviously, if you start with an even number of down cups, it’s easy to win, just going down the line.)

No, I think I got that. I guess it’s one of those things that would seem pretty obvious. Then again, I guess bar bets are like that. Wouldn’t your mark notice that one move makes all three cups up in the second situation?

edit: Ah, I think I see the point. You do it in three moves, not one (even though it’s possible in one) to confuse your sucker. Or am I still not getting it?

Ah, yeah, I see now that the post you were responding to said “three turns” for something that’s clearly possible in one turn, and that’s what you were talking about the whole time. I misunderstood your confusion.

So, yeah, your mark would have to be pretty dumb. But, I guess, as you do, that maybe you can confuse them by making unnecessary use of three moves rather than one.

The three turns rule also helps confuse the opponent and help them forget the original configuration of the cups, so that when you reset them, it’s less obvious that you’re starting off with a different arrangement of cups.

If the opponent notices that you can win by just flipping over two in the first turn, you say “yes but remember the three turn rule, that’s what gave you so much trouble!” Oh, right!, he says.

Remember, we’re in a bar with empty shot glasses in front of us. You’re counting on somebody being a bit sloshed for this to work. I think it might even work with sober people since most just aren’t that observant.

You could also add the rule that the two cups you turn over on each turn have to be next to each other, which eliminates the “just flip the two on the ends” solution. It’s still pretty easy, but just complicated enough that it might confuse a drunk.

If you do that, it’s impossible to pull it off in exactly three turns… after your first turn (with the cups starting off D U D), the cups would be U D D, and you’d have to either solve it right away or undo what you just did.

But, yes. There are myriad ways to confuse a drunk.

Three turns…three cups.