Problem #$2$: The Five Hats Problem $($Analyzing the Problem State$)$

Given the following problem statement and constraints, determine how the blind man knew which color hat he was wearing and explain how he knew.

Three men are condemned to die, one of whom is blind.

The king decides he will offer them an opportunity to be set free.

The three men are arranged in a circle facing one another.

The king produces $5$ hats: $2$ black and $3$ white.

The king places a hat on the head of each person and then destroys the two remaining hats.

The men have no idea which hats have been destroyed.

The king instructs them, "The first one of you who can tell me the color of his hat will be set free."

A period of time passes in silence and then finally the blind man tells the king the color of his hat and is set free.