Originally Posted by serfty
Ok, How about this?:
SYD-1-HKG-2-LHR-3-<3 europe segs>-7-<4 NA segs>-12-<3 Asia segs>-16-MEL-17-PER-18-MEL-19-BME-20-SYD
That is valid, provided that the NA and Europe segments meet their respective rules (e.g. only one NA transcon flight and no trip to HNL in your case as you'd have to go on to SYD as the only available flight and that then ends your RTW when you reach your city of origin).