## Skeleton Towers

#### Problem

Skeleton towers are generated as follows.

How many blocks would be needed to construct the 100th tower?

#### Solution

It is possible to split a tower in the following way.

And so the 100th tower can be made into a 100 100 square, requiring 10,000 blocks.

One way of constructing three dimensional skeleton towers is as follows.

How many blocks would be needed to construct the 100th tower now?

Problem ID: 53 (Nov 2001) Difficulty: 1 Star