Consider 2 nations, A,B which have found a brand new planet, the dimensions of earth.

They have determined to separate the planet into areas of minimal space $10^3 m^2$ and most space $10^5 m^2$ with contiguous border (the area shouldn’t be break up into a number of elements which can be separated). They can declare a area of requested form and space anyplace on the planet so long as it doesn’t overlap with every other area beforehand claimed. They additional alternate in choosing areas. They resolve A goes first. Then B, then A and so forth (alternating picks).

Further, there’s provision to reward the higher strategist: whoever locations the final area, will get the opposite nation’s smallest area as a reward. Which nation will get extra land? Explain clearly why and the way.

Bonus: Is it potential to calculate the full closing space of every nation? If so, what’s it? You are welcome to imagine that the planet is an ideal sphere for the whole query.