1. Combinatorics (condition):
The tiler must lay out a strip of 2 × n squares. And with tiles that are always made up of two squares of a tile strip (a 1x2 rectangle) and tiles of four different colors (both squares of each tile have the same color). In how many ways can a tiler pave a 2 × n strip?
(Instructions: set a recursive prescription for the problem and solve with recursion.)
2. Graph theory (condition):
Find all non-isomorphic induced subgraphs at six vertices of Cn for n ≥ 12.
The individual steps of the procedure must be carefully explained.
You must complete this task by Monday 23:59 Paris time.
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