Singapore > Xiamen > Hong Kong > Singapore

Sarah, your itinerary is definitely eligible for 240 hour visa free transit and you can proceed with your travel plans with absolute peace of mind. My main sources are official websites of the Chinese authorities and especially the one of the Chinese National Immigration administration. Also, I am in the subject of visa free transit already for 8 years, so this is quite an experience. For example, I always tell the people to check their itineraries, if they are not certain, with the said website where they can also use a chat option. In any case, have a nice visit to China.