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The answer depends on the grid. On the taxicab grid, which was studied by Minkowski, the distance is the sum of the vertical and horizontal distances between a and b. See, for example, https://en.wikipedia.org/wiki/Taxicab_geometry

If, a and b have horizontal and vertical coordinates which are, respectively, (xa, ya) and (xb, yb) then the grid distance is abs(xa - ya) + abs(xb - yb).

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Q: The distance from point a to b on a grid?
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