Magic Hat of Consecutive Numbers
Alright, this one may be the puzzler of the millennium, no pressure.
We’ve got a magic hat and two contestants: you and Vinnie.
Each of you pulls out a number. Here’s the twist: Your numbers are always one apart.
So if you pick 3, Vinnie has either 2 or 4.
I ask you: “Do you know Vinnie’s number?”
You say, “No.”
I ask Vinnie: “Do you know Tommy’s number?”
He might say yes… or no.
We keep going back and forth, each time asking, “Do you know the other guy’s number?”
Eventually—after enough “no’s”— one of you suddenly knows the other’s number for sure.
Why does repeated questioning eventually guarantee that one of them figures it out?
