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# etch-a-sketch math

## Question

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?

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I think the endpoints would look like...

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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?

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The knobs won't turn beyond the boundaries

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

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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.

+ o + o + o + + | + + + + + + + +
o + o + o + o + | + + + + + + + +
+
o + o + o + o | + + + + + + + +
o + o + o + o + o + + + + + + + +
+
o + o + o + o | o + + + + + + +
o O o + o + o + o + o + + + + + + O = Starting point
+ o + o + o + o | o + + + + + + + o = landing points

o-+-o-+-o-+-o-+-o-+-+-+-+-+-+-+-+

+ o + o + o + o | + + + + + + + +
o + o + o + o + | + + + + + + + +
+ o + o + o + + | + + + + + + + +
o + o + o + + + | + + + + + + + +
+ o + o + + + + | + + + + + + + +
o + o + + + + + | + + + + + + + +
+ o + + + + + + | + + + + + + + +
+ + + + + + + +
| + + + + + + + +

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