For each country, give the name of the country that is closest to it. The distance between them is the one between their geographical centers
Data from Portland State University (https://www.pdx.edu/econ/country-geography-data), for missing countries from CIA (https://www.cia.gov/library/publications/the-world-factbook/fields/2011.html)
I would say Indonesia is closer to Papua New Guinea than The Solomon Islands is to Papua New Guinea, as Indonesia borders Papua New Guinea on the island of New Guinea.
You're certainly right, however I have no data on 'distance between countries', this quiz is based on 'distance between geographical centers of countries'; since Indonesia is so big, its 'center' is actually quite far from Papua New Guinea