This chart >>>
http://chartsbin.com/view/wwu <<< shows the Total Surface Area (TSA) of the Earth. Since 70.8% of Earth's surface is water (both fresh and salt), this means that there is 29.2% left over for land. If you were to give everyone 25% of the total surface area of the earth, it would be 85.62% of all of Earth's land. Even then, not all of that is habitable, but I'll address that in a bit.
From this article >>>
http://www.universetoday.com/25756/surface-area-of-the-earth/ <<< we can assume that the TSA of Earth's land is 149 million square km as quoted in the article. 85.62% of 149,000,000 is 127,573,800 square km. Further divide that by 20 billion (20,000,000,000) and you get this:
6.37869x10^-3 square km for every person out of those 20 billion. That's 0.00637869 square km, which (using
an online converter) equates to
6378.690m² per person.
That's much, much more than the minimum 100 square meters (10x10=100) that you specify in your post, Hampus... so by these calculations, everyone gets a pretty fair deal!
However (and this is what I briefly mentioned earlier):
The chart in my first link notes that only 8.76% of Earth's total TSA is farmable. Everywhere else is essentially inhospitable. If you want everyone to be able to live off the land they own, it must be this farmable land. So let's alter the calculations a bit to take this into account.
8.76 out of 29.2 is 30% of Earth's land TSA. 30% of 149,000,000 is 44,700,000 square km.
Divide 44,700,000 by 20,000,000,000 and you get 2.235x10^-3 square km per person. That is 0.002235 square km per person, which when fed through the converter is
2235.0m² per person.
Which is still a lot more than 10x10 metres. Give everyone their own little water supply and they'd still have more space than that to live in.
So, long story short - whichever way you look at it -
Yes, Hampus, it's possible.
(Dammit, I should be in bed right now...)