Thanks a lot for this very well detailed answered. You demonstrate exactly why I love asking this kind of problems. There is no unique answer and there are gazillions of ways to go through the problem. Everything you said is correct, and the problem was made intentionally short (so that the challenge has a chance to last for a week). I was planning to give more information with the comments.

Here are more specifications (I will edit the post accordingly):

• we just want to lift the house out of the ground by few centimeters. We don't assume it is fixed although this would have made the problem even more complicated to realize in practice as more balloons would be needed.
• We consider a real house and real balloons.
• The picture is more illustrative than anything else.
• We make the crude and wrong assumption that all balloons can be inflated simultaneously in no time.

As I said, this is not realistic but this is for the fun of the challenge!