MathDB

We have a white table with

2

rows and

5

columns , and would like to colour all cells of the table according to the following rules:

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We must colour the cell in the bottom left corner first.

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After that, we can only colour a cell if some adjacent cell has already been coloured. (Two cells are adjacent if they share an edge.)
How many different orders are there for colouring all

10

squares (following these rules)?

Problem Statement