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This problem encourages students to think about vectors as representing a movement from one point to another. The need for coordinate representation of points will emerge automatically and the problem naturally requires an interplay between geometry and algebra.
What do the points you can reach with $b_1$ and $b_2$ have in common?
Work systematically combining $b_1$ steps with $b_2$ steps, recording the points visited.
Polygon Walk explores vector walks which form polygons around the origin.