The Alien's Crystal

Logic Level 3

You and your 2 traveler companions have just discovered an ancient alien hideout on a ghost planet. A single alien comes out to greet you.

The alien has a valuable crystal that he wants to give to the smartest of your group. So, he devises a completely fair intelligence test.

You and your companions are brought to a room and seated, facing 1 another, and are shown 2 green hats and 3 blue hats. Then, you are all blindfolded, and 1 hat is placed on each of your heads, with the remaining hats hidden in a different room.

The alien tells you that the first traveler to figure out the color of their hat without removing it or looking at it will get his crystal. A wrong guess will mean death. Your blindfolds are then removed.

You see 2 blue hats on the other traveler's heads. After some time you realize that the other travelers are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat?

Note: You know that your companions are very intelligent and very much want to have the crystal. You also know that the alien is an alien of his word, and he has said that the test is a fair test of intelligence and bravery.

Green Not enough information Blue

Michael Huang by Michael Huang , 17, USA

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3 solutions

Jay Singh
Apr 22, 2018

If the other two are unable to deduce which hat they are wearing, that must mean that they too see two blue hats, meaning you are wearing a Blue hat.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Michael Huang
Apr 11, 2018

The alien would not pick 2 blue hats and 1 green hat. This would mean 2 of the travelers would see 1 green hat and 1 blue hat. You would be at a disadvantage if you were the only traveler wearing a green hat.

If you were wearing the green hat, it would not take long for 1 of the other travelers to deduce he was wearing a blue hat.

If one of the travelers saw a blue hat and a green hat, he can deduce that the alien would never select 2 green hats and 1 blue hat. Any traveler seeing 2 green hats would instantly know he was wearing a blue hat. Therefore, if a traveler can see 1 green hat, he can work out he is wearing blue.

Therefore, the only fair test is for all 3 travelers to be wearing blue hats.

After waiting some time just to make sure, you can safely say that you are wearing a Blue \boxed{\text{Blue}} hat.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

But the other companions will also know the color of their hats,too,because they know the alien is fair?

X X - 3 years, 2 months ago
Siva Budaraju
Apr 11, 2018

If your hat wasn't blue, it wouldn't be fair as different people would see different things.

2 Helpful 0 Interesting 0 Brilliant 1 Confused

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