Win the Bar Bet: Another Sucker Trick

[soroban]

A good bar bet (but wear running shoes).

Get three glasses.
Arrange them like this: $\;\begin{array}{ccc}\cap&\cup&\cap\\ ^1&^2&^3 \end{array}$

Challenge

On each turn, invert two glasses.
In three turns, get the glasses face up.

You demonstrate this quickly.

$$\begin{array}{cc}\text{Starting position:} & \cap\;\cup\;\cap \\ \text{Invert 1 and 2:} & \cup\;\cap\;\cap \\ \text{Invert 1 and 3:}& \cap\;\cap\;\cup \\ \text{Invert 1 and 2:} & \cup\;\cup\;\cup \end{array}$$

You say "Got it?"
and invert the middle glass: $\;\cup\;\cap\;\cup$
Then say, "Okay, you try it."

He will always fail.
Note that his starting position
. . is not the same as yours!

 

[kaliprasad]

in each inversion the number of glasses up goes up or down by 2 but we need to make it up by 1 and it cannot be done in any number of inversions.