A good bar bet (but wear running shoes).
Get three glasses.
Arrange them like this: \(\displaystyle \;\begin{array}{ccc} \\ \cap&\cup&\cap\\ ^1&^2&^3 \end{array}\)
Challenge
On each turn, invert two glasses.
In three turns, get the glasses face up.
You demonstrate this quickly.
\(\displaystyle \begin{array}{cc}\text{Starting position:} & \cap\;\cup\;\cap \\
\text{Invert 1 and 2:} & \cup\;\cap\;\cap \\
\text{Invert 1 and 3:}& \cap\;\cap\;\cup \\
\text{Invert 1 and 2:} & \cup\;\cup\;\cup \end{array}\)
You say "Got it?"
and invert the middle glass: \(\displaystyle \;\cup\;\cap\;\cup\)
Then say, "Okay, you try it."
(Remind him: 3 turns, face up.)
He will always fail.
Note that his starting position
. .is not the same as yours!