Question 161
The L shape made by adjoining three congruent squares can be subdivided into four smaller L shapes.
Each of these can in turn be subdivided, and so forth. If we perform 2005 successive subdivisions, how many of the $4^{2005}$ L's left at the end will be in the same orientation as the original one?
Each of these can in turn be subdivided, and so forth. If we perform 2005 successive subdivisions, how many of the $4^{2005}$ L's left at the end will be in the same orientation as the original one?