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# Logical Reasoning

How can you find a fake coin with a balance scale? How can you use math to pretend to read minds? Solve these puzzles and build your foundational logical reasoning skills.

Three people are in a room wearing hats. Two of them are wearing blue hats and one of them is wearing a red hat; they can't see what color hat they are wearing, but they can see everyone else's hats. They are playing a game where their objective is to figure out the color of their own hat. (You can assume with this question and any other in this quiz the players will know how many hats there are and in which colors.)

If a player sees the other two players have a red hat and a blue hat, what color hat are they wearing?

Suppose Amy, Bo, and Cid are playing a game. Assume the players are -- and know each other are -- perfect at logic.

There are two red hats and two blue hats available. The players are blindfolded and each person is given a hat to wear such that when their blindfold is removed they can't see their own hat.

They are put in a line so Amy can see Bo and Cid, but Bo can only see Cid, and Cid can't see anyone. Then their blindfolds are removed.

Amy says, "I don't know what color hat I'm wearing."

Then Bo says, "I must be wearing blue."

What color hat is Cid wearing?

Suppose Amy, Bo, and Cid, and Dina are playing a game. Assume the players are -- and know each other are -- perfect at logic.

There are two red hats and two blue hats available. The players are blindfolded and each person is given a hat to wear such that when their blindfold is removed they can't see their own hat.

They are put in a line so the players can see the person (or people) immediately next to them but nobody else. Their blindfolds are then removed.

Bo says, "I don't know the color of my hat."

If it is later revealed that no players next to each other are both wearing blue, what color hat is Amy wearing?

Suppose Amy, Bo, and Cid and Xenia are playing a game. Assume the players are -- and know each other are -- perfect at logic.

There are two red hats and two blue hats available. Amy, Bo, and Cid are blindfolded and each person is given a hat to wear. Xenia doesn't wear either a hat or blindfold and can see all players at all times.

None of the blindfolds are removed.

Xenia is, however, allowed to talk to any of the three players by saying either "Yes" or "No"; all the players will know who Xenia was talking to.

How many words must Xenia say before all the players can work out the color of their hat? (Assume the players have a chance to plan before the game starts.)

Three people are in a room wearing hats.

Either two of them are wearing blue hats and one of them is wearing a red hat

OR

two of them are wearing red hats and one of them is wearing a blue hat.

They can't see what color hat they are wearing, but they can see everyone else's hats. They are playing a game where their objective is to figure out the color of their own hat. The players are not allowed to talk during the game.

If a player sees the other two players have a red hat and a blue hat, what color hat are they wearing?

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