Notes from the underground
barang dot sg
Updated 2 December 2023
36. Three white hats

Three logicians
Three equally-skilled logicians sit in a circle. A hat is placed on each of their heads. Each logician can see the hats of the two others but not his own.

They are now told that:
1) Each hat is either white or black
2) At least one hat is white
and are invited to deduce the colours of their own hats.

In fact, all three hats are white and it isn’t long before the three of them simultaneously announce, “My hat is white.”

How did they deduce this?

Bonus puzzle. Each logician could already see two white hats, so statement 2) above told them something that they already knew. What for?