Course 5655
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We consider a variation on Euler Problem 215.
Walls are still built out of 2x1 or 3x1 bricks, but this time is it OK to have "running cracks" of length at most 2, as in the following 9x3 wall:
However, longer running cracks are disallowed. The following 9x3 wall is not acceptable because it has one running crack of length 3.
There are possible 9x3 walls in which the maximal length of running cracks is 2 or 1.
There are possible 10x4 walls in which the maximal length of running cracks is 2 or 1.
There are possible 11x5 walls in which the maximal length of running cracks is 2 or 1.
Compute the value of .
Hint: consider a graph whose vertices represent pairs of layers, such that an edge represents in acceptable superposition of the three layers , , and .
Consider the 90280 configurations of the 2x2x2 Rubik's cube that require exactly 13 quarter turns to be solved optimaly.
How many of those have the front face entirely white?
(You should assume the white square with the Rubik's cube logo is always on the front face, as we did in the video.)