Question 95
As shown in the figure, seven regular hexagonal cells form a hexagonal pattern. We write one integer from $1$ to $7$ in each cell without repetition. For any two cells that share an edge, the sum of the integers written in those cells must be at most $10$. How many ways are there to write the integers under these conditions?
Note that two labelings that coincide by rotation or reflection are counted as distinct ways.
Note that two labelings that coincide by rotation or reflection are counted as distinct ways.