### Brain Teasers

# Pick A Conclusive Statement

Eli and four of his friends either always lie or always tell the truth. His friends made the following statements:

Alice: Daniel or Eli is lying

Barry: Eli, Daniel, & Callie are telling the truth

Callie: Daniel is lying

Daniel: Callie and/or Barry is lying

Eli said one of the following things:

Alice & Barry are opposites (one lies and one tells the truth)

Alice & Daniel are opposites

Barry & Callie aren't opposites

Callie & Myself aren't opposites

If you knew which of the four statements was spoken by Eli, then you would know who was lying and who was telling the truth. What did Eli say? Who is lying?

Alice: Daniel or Eli is lying

Barry: Eli, Daniel, & Callie are telling the truth

Callie: Daniel is lying

Daniel: Callie and/or Barry is lying

Eli said one of the following things:

Alice & Barry are opposites (one lies and one tells the truth)

Alice & Daniel are opposites

Barry & Callie aren't opposites

Callie & Myself aren't opposites

If you knew which of the four statements was spoken by Eli, then you would know who was lying and who was telling the truth. What did Eli say? Who is lying?

### Answer

Barry & Callie aren't opposites; Alice, Barry, & Callie are lying.First figure out who you can figure out before you even go to Eli's statements.

Assume Barry was telling the truth

Daniel is telling the truth

Callie was telling the truth

Therefore Daniel is lying

Which is a contradiction

So Barry is definitely lying

Which means Daniel is telling the truth

Which means Callie is lying

We can't know Alice's or Eli's position yet.

If Eli says Alice & Barry are opposites & Eli is honest, then Alice is honest.

If Alice is honest then Eli is lying because Daniel isn't lying.

That's a contradiction.

If Eli is lying then Alice is lying, and Eli is telling the truth.

If Eli says Callie & Myself aren't opposites, then Eli is basically saying that he himself is a liar, which is a contradiction.

If Eli said Alice & Daniel are opposites & is telling the truth, then Alice is lying & Eli is telling the truth.

If Eli said Alice & Daniel are opposites & is lying, then Alice is telling the truth & Eli is lying.

There is no way to conclude who is lying, but Eli's statement is conclusive, therefore it can't be this.

If Eli said Callie & Barry aren't opposites, then he would be telling the truth & Alice would be lying.

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