Flying in and out of China can use visa free twice?

I have a flight booked to and from China but will land and fly out to a third country. If I stay less than 24 hours in China both for my flight in and two weeks later for my flight out can I do this without a visa? Is it ok to use the 24 exemption two weeks later? I'm flying in and out of Beijing Capital would I be able to use the 72 hour free transit rule both times as well or will it not allow two separate uses?