Country Connect: Closest Neighbour with Disappearing Map
Start in Antarctica. Move to the closest country. From there on move to the 'closest' country that hasn't been visited yet. This means the neighbour with which it shares a longer border or the closest country if there are no neighbours left.
Numbers indicate length of border (if in plain text) or distance to closest non-neighbour (if in bold italics)
Borders on territories are considered
Distances are in km
Data from here and some quizzes by Jerry928 and Wikipedia
To be fair to you, it's not to the Australian mainland: I *think* that's to Macquarie island, a tiny rock with no permanent population south of New Zealand, but I don't even get the same distance as is on the quiz when I try and measure.