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HMMT Nov — Five Guys Truth/Lie Logic Puzzle

1675AdeptCombinatoricsAlgebraCasework

2nd Annual Harvard-MIT November Tournament

There are five guys named Alan, Bob, Casey, Dan, and Eric. Each one either always tells the truth or always lies. You overhear the following discussion between them: ``` Alan: "All of us are truth-tellers." Bob: "No, only Alan and I are truth-tellers." Casey: "You are both liars." Dan: "If Casey is a truth-teller, then Eric is too." Eric: "An odd number of us are liars." ``` Who are the liars?
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