Impossible

[init1]

This is impossible, right?
http://www.albinoblacksheep.com/flash/3cup

[brharri1]

I think it starts opposite what it shows you.

[steveneddy]

The way it shows you how to solve the puzzle, the cups are actually backwards from when they give you the cups to try and solve the puzzle.

They show you how to solve it with the middle cup up, then give you the puzzle to solve with the middle cup down.

Possibly impossible.

[illu45]

Yup. If you watch carefully, in their demo, the middle cup faces up. When you start, it faces down, making it impossible to get the cups to face up. Nice music, though.

[croto]

Yep, it's impossible. Here's a proof:

First let's assign numbers to cups positions: cup up = 1, cup down = 0. Then if you have two cups up and one down, for instance, the total sum is 2. If you have three cups up, the sum is 3, and so on. It is obvious that by flipping to cups, the parity of the total sum is conserved (check it!). Therefore, if you start with two cups up and one down, the parity is even (sum=2). There's no way to go to three cups up, because it has odd parity.

[init1]

I wasted way to much time trying to figure it out. It's nothing more then a prank.

[teet]

Yep, it's impossible. Here's a proof:

First let's assign numbers to cups positions: cup up = 1, cup down = 0. Then if you have two cups up and one down, for instance, the total sum is 2. If you have three cups up, the sum is 3, and so on. It is obvious that by flipping to cups, the parity of the total sum is conserved (check it!). Therefore, if you start with two cups up and one down, the parity is even (sum=2). There's no way to go to three cups up, because it has odd parity.

Nice. It took me a good twenty minutes to realize they were playing the old "switcheroo" on me. I actually have up/down arrows scribbled across a piece of paper trying to figure this out. Your proof is a lot easier and puts my mind to rest.

-teet