etch-a-sketch math

[BMAD]

I have two points on a cartesian plane with bounds from (-8,8) for x and y. One point is at (-7,2). I drew a line from this point to another point using etch-a-sketch moves (left/right) and (up/down). Each turn of a dial is a one unit move. I moved the dials a total of nine times. What are alll the possible endpoints?

[gavinksong]

I think the endpoints would look like...

[bonanova]

What happens at the boundaries?

Do you prohibit moves that would cross them, or like a real E-a-S, just ignore the turning of the knob?

[BMAD]

The knobs won't turn beyond the boundaries

[BMAD]

Bear in mind that I don't mean a straight line necessarily. Just a connected set of line segments

[bonanova]

Fifty-nine landing points,

having integer coordinates that sum to an even number lying within (x, y) e[-8, 8] and

bounded by the portion of a diamond of diameter 18 centered on the starting point.

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