Tony Stark wants to build a 1000 meter high tower as quickly as possible. He has unlimited resources and an unlimited budget and is willing to spend any amount to get the job done. He has chosen to build the tower with blocks that are 100 meters long and 100 meters wide, but only 1 meter tall. The blocks interlock on top and bottom (like legos). They cannot be stacked sideways.

Using special lifters, putting one block on top of another block takes one week. Putting a stack of up to 100 blocks on top of another stack of 100 or less also takes a week. If either stack is more than 100, it takes two weeks.

What is the shortest amount of time that it will take to build the tower?
Why is your answer the shortest amount of time?
How did you solve the problem? What is your algorithm?