### Brain Teasers

# Eight People

In a mathematics contest, A, B, C, D, E, F, G and H got the top eight places. The teacher asked them to guess who got first.

A said: "Either F or H is first."

B said: "I'm first."

C said: "G is first."

D said: "B is not first."

E said: "A is wrong."

F said: "Neither I nor H is the first."

G said: "C is not first."

H said: "I agree with A."

The teacher told them that exactly three of them guessed correctly. Then, who got first?

A said: "Either F or H is first."

B said: "I'm first."

C said: "G is first."

D said: "B is not first."

E said: "A is wrong."

F said: "Neither I nor H is the first."

G said: "C is not first."

H said: "I agree with A."

The teacher told them that exactly three of them guessed correctly. Then, who got first?

### Hint

It's OK to use trial and error, however, there might be better methods.### Answer

Since B and D contradict each other, exactly one of them must be true.Since A and H agree with each other while E and F are against them, exactly two of these four must be true.

Therefore, neither C nor G guessed correctly. Since G guessed that C is not first, C must be first.

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