Teacher writes a four-digit number on paper and Tom guesses what number it is.  Tom asks: "Is it $$8765$$?"  Teacher says: "Two of the digits are right, but they are not in the right digit position"  Tom asks: "Is it $$1023$$?"  Teacher says: "Two of the digits are right, but they are not in the right digit position"  Tom asks: "Is it $$8642$$?"  Teacher says: "Two of the digits are right, and they are in the right digit position"  Tom asks: "Is it $$5430$$?"  Teacher says: "None of them is right".  What\textquotesingle s the $$4$$-digit number? 
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