Start at the south pole, then jump to the closest country starting with J, then from there to the closest country starting with E, etc.
Repeat for the equator and north pole.
I agree. I couldn't understand how, if Jamaica is closest to the South Pole, it isn't also closest to the Equator. I know that will spoil the quiz, though!
If the distances are between capitals.. are those the distances being used to determine which country is closest to the next country? If not, you should really specify that you're apparently not considering overseas territories, and regardless you should really specify that the distances are in km.
Please use the "Auto" type-ins (for United States, for example). The J for Equator category is still incorrect, it might work to replace it with the Prime Meridian. North Macedonia should also be on here.
Fun quiz!