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Astra, Breach and Cypher each say something about their numbers of cats, truthfully to anyone with more cats and falsely to anyone with fewer. How many cats does Breach have?

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Astra, Breach and Cypher have different numbers of cats. (a) Cypher tells Breach: 'You have an even number of cats.' (b) Breach tells Cypher: 'You have exactly 40% more cats than me.' (c) Breach tells Astra: 'Your number of cats is the average of mine and Cypher's.' (d) Astra tells Breach: 'I have at least 3 more cats than you.' Not all statements are true: a speaker talking to someone with more cats always tells the truth, and talking to someone with fewer cats always lies. How many cats does Breach have?

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