A grid must have a mechanism for numbering the tiles in order to support random-access search. A square grid, for example, contains rows and columns that provide a natural numbering for the tiles. Create designs for triangular and hexagonal grids. Define a rule for finding the neighbourhood (i.e. nearby tiles) of a particular tile in the grid using the numbering scheme. For example, if we have a four-connected square grid with indices I for rows and j for columns, we may define the neighbourhood of tile I j as neighbourhood(i, j) = I 1, j,i, j 1.

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