1. There is a piece of paper with a thickness of 0.1mm. How thick will it be if it is folded in half for 20 times in a row? Please guess, is the building about 3 meters higher than the 30-story building thicker?

After folding for 20 times, the height is: 0.1* 220/100 =1048576m.

The height of 30 floors with each floor of 3m is: 3 * 30 = 90m.

So the thickness of paper is higher than that of buildings.

2. Bicycle tires are scrapped after running 5000 kilometers with front wheels. If installed on the rear wheel, it can only run 3000 kilometers. If you want to travel as much as possible, you can change the front and rear tires when the bicycle travels to a certain distance. How many kilometers can a pair of new tires installed on a bicycle travel at most?

When changing tires, the bicycle will travel x meters. If it is not changed, the front wheels will be scrapped after traveling 5000-x meters and the rear wheels will be scrapped after traveling 3000-x. At this time, when changing tires, the front wheels can only travel (5000-x) * (3000/5000) = 3 (5000-x)/5, and the rear wheels can travel again (3000-x). Therefore, there are:

3(5000-x)/5=5(3000-x)*3, x =1875m, that is, the bicycle went1875m when changing tires.

After the tire was changed, the bicycle left again: 3 (5000-1875)/5 = 5 (3000-1875) * 3 =1875 meters.

In this way, the bike went 1875+ 1875=3750 meters.