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1 For tomorrow, think about the questions we raised in class:
Does a piece that can move up/down or diagonally with a slope of 1 get to anywhere on the plane? Yes. It can move to any point on the y axis from any point on the y axis, and can move to any point on the x axis by creating a independent x axis move with one over diagonally and one down.
What other possible move choices will allow a piece to go anywhere on the plane? Any move sequence which can create an orthogonal move by one unit. E.G. Knight: 2x+1y, 1y-2x, 1x-2y = 2x-2x+x+y+y-2y = x
What about in THREE SPACE?? Should be able to just expand to higher dimensional spaces..
For next MONDAY, read 1.C!