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Omni-MATH / The L shape made by adjoining three congruent squares can be subdivided into…

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problem

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 420054^{2005} L's left at the end will be in the same orientation as the original one?
Plain-text mathematical notation (without MathML)
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 4²⁰⁰⁵ L's left at the end will be in the same orientation as the original one?
Original LaTeX notation
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?

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Source and history

task_id
bdcb02a7-e0ec-50e2-8871-40c070fd6f72
task_key
test--bdcb02a7-e0ec-50e2-8871-40c070fd6f72
task_revision_id
1
config / split
/ test

Official source

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