Do I qualify for 72- hour Visa-free transit

U.S. Citizen flying to Singapore from USA. for Cruise to Hong Kong,
Stay in Hong Kong 18 hours. (No Visa required?)
Fly out of Hong Kong non stop to Beijing.
Stay in Beijing City less than 72 hours.
Fly out Beijing to Seattle Wa.USA.
Would I qualify.
Also Would the Visa qualify for a tour of the Great wall near Beijing .
Thank You!