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ASU 270 All Soviet Union MO 1979 grasshopper hopping on cartesian

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July 11, 2019
coordinatesareascombinatorial geometry

Problem Statement

A grasshopper is hopping in the angle x≥0,y≥0x\ge 0, y\ge 0 of the coordinate plane (that means that it cannot land in the point with negative coordinate). If it is in the point (x,y)(x,y), it can either jump to the point (x+1,y−1)(x+1,y-1), or to the point (x−5,y+7)(x-5,y+7). Draw a set of such an initial points (x,y)(x,y), that having started from there, a grasshopper cannot reach any point farther than 10001000 from the point (0,0)(0,0). Find its area.
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