36. Three white hats

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?