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What color hat?
Uncle Bill, the teaser, had his 2 nephews and 1 niece over. He brought out 5 hats, 2 of them red, 3 of them white. He
blindfolded the kids and put a hat on each of their heads. Bill said that they each need to make a guess of the color of the
hat on his or her head, and he'll take off the blindfolds one by one for the guesser. He said if any one of them
guesses correctly, he'll take them to the amusement park. If no one guesses, he'll have them clean up the yard. Tom, the oldest,
decided to try first. The blindfold came off and he looked at the hats on his brother and sister, but admitted he didn't
know the color hat he was wearing. Joey said he'd go next. His blindfold was removed and he could not figure out
the color of his hat he was wearing. Stacy then said she knew the color of the hat on her head without needing her
blindfold taken off. Did the kids have to clean the yard or did they get to go to the amusement park? What color
hat did Stacy have on?
The answer is "They got to go to the amusement park, and Stacy had a white hat on." She reasoned it like this:
When Tom took off his blindfold, he would have guessed "white" if Stacy & Joey both had red hats, since there
were only two red hats. Since he didn't know, then Stacy & Joey each have a white hat, or have a red and a white. When Joey's turn
came, he would know that either he (Joey) or Stacy, or both - are wearing a white hat, from Tom's confusion. Since Joey sees
Stacy's hat and still doesn't know his hat color, she knows that she and Tom did not both have a red hat on.
The choices left then are:
Name, W=white, R=red
Tom --- W W R R
Joey --- W R W R
Stacy -- W W W W
Every choice left leaves Stacy with a white hat.
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