hat trick

[westworld]

Alice stands facing a wall, Bob stands behind Alice, Carol is behind Bob, Dave is behind Carol, and Eve is behind Dave. All five are facing the wall.

The five are blindfolded and three white hats and two black hats are placed on their heads. When the blindfolds are removed each person can see all the hats in front, but not his or her own hat or any of the hats behind.

Dave says, "I do not know what color my hat is." Bob replies, "Well, I know what color mine is." Then Alice says, "I know what color my hat is too."

 

[soroban]

Hello, westworld!

Alice stands facing a wall, Bob stands behind Alice, Carol is behind Bob,
Dave is behind Carol, and Eve is behind Dave. .All five are facing the wall.

The five are blindfolded and three white hats and two black hats are placed on their heads.
When the blindfolds are removed, each person can see all the hats in front,
. . but not his or her own hat or any of the hats behind.

Dave says, "I do not know what color my hat is."
Bob replies, "Well, I know what color mine is."
Then Alice says, "I know what color my hat is too."

What color were their hats?

Drag your cursor between the asterisks.

**

If Dave saw WWW, he'd know his hat was Black.
If Dave saw WBB, he'd know his hat was White.
. . He must have seen WWB in front of him.

Bob knows all this.
If he saw a White hat on Alice, he could have a White or Black hat.
Since Bob knew his color (White), Alice must have the Black hat.

Alice followed the same reasoning
. . and knew she had a Black hat.

**