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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Comments
Inspired by "Sore Losers" multi-solving set-up.
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