There are 8 blocks, consisting of two cubes (black and white), and a platform for constructing special things. One of the blocks is glued to the platform as shown in the picture to the left. How many ways can the structure be completed to the one shown in the picture?Task_picture

So, the main point of this task is to find the number of complete matchings. My point of view: First of all, we can expand the cube and number each of the smaller "cubes", according to their color and dependencies:Expand_picture

After that we can make an adjacency matrix for such a graph (for example, if we place a block to the "1 black", we can occupy 4, 6 and 1 white blocks).


Then, we should calculate the permanent of this matrix per(M) and this will be the answer. Also, the answer is 7. Is it right way of thinking? Is there an easier way to calculate such task?


closed as off-topic by Yoav Kallus, Ivan Izmestiev, Max Alekseyev, Chris Godsil, user44191 May 13 at 18:18

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