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Deductive Thinking Hat Puzzle

Deductive Thinking Hat Puzzle - 18 December

Four friends are sitting on a tree. Each one of them are wearing a hat. They dont know which colored hat are they wearing but they do know that two of them have green hats and two of them have orange hats.

Adam is sitting on the top branch and he can clearly see the hats of Billy and Cyrus. Billy is sitting on a branch above Cyrus and he can see Cyrus hat clearly. Duke is sitting at the base of the tree. There are branches covering him fully and no one can see his hat.

Now they are nota allowed to look upwards. Who do you think will shout the color of his hat first?

For Solution : Click Here


  1. If Adam sees 2 hats of the same color ,he can deduce that he has a hat of the other color, so he shouts his color. If he sees two different colors he can't be sure, so he stays silent. In this case ,Billy can deduce that since Adam stayed silent , he and Cyrus must have opposite colors and thus he knows his color and shouts it.
    Probability that Cyrus' and Billy's hats are both green or both orange is 2/4 (possible coloring :OO,GG,OG,GO) . So it is exactly 50-50% chances between Adam and Billy.

  2. yes billy would shout first

  3. Adam will shout that orange color hat

  4. Assuming they're all cheaters, they would shout out the color of their hats altogether without having to look up, they would simply take their hats off to look at the color. Lol. No really, I think the first comment makes a lot of sense. Good chance that it will be Billy because if Adam stayed silent then yeah, he'll know he and Cyrus had different color hats. So if Cyrus has an orange one, he'll know for sure that his is green. This is a really fun and challenging riddle. You should do more of this. This actually is a better exercise for the brain rather than just updating social media profiles.

  5. billy will shout first. if he and cyrus wears same colour hat then adam shouts.if not than adam will take some time to figure out. in the mean time ,billy will be sure that which colour hat is he wearing and it is different than that of cyrus's colour.