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Since there are $100$ floors and the number of Mary's apartment is equal to John's floor's number, Mary lives at most at apartment $100$ , so John's apartment's number is at least $2017 - 100 = 1917$ and at most $2017 - 1 = 2016$ . This means he lives between floor $77$ and floor $81$ , which means Mary's apartment's number is between $77$ and $81$ . Consequently, John's apartment's number is $1936$ , $1937$ , $1938$ , $1939$ or $1940$ ( because the sum of their apartment's numbers is $2017$ ), which are all in floor number $78$ . Therefore, John's apartment's number is $2017 - 78 = 1939$ .