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Math Help - Frog question on vertices

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    Frog question on vertices

    Three frogs are placed on three vertices of a square. If the frogs can "leapfrog" over one another in such a way that the frog who was leaped over is at the midpoint of the line segment made by the frog who leaped, will a frog ever occupy the original empty vertex of the square?
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    Quote Originally Posted by mathman7 View Post
    Three frogs are placed on three vertices of a square. If the frogs can "leapfrog" over one another in such a way that the frog who was leaped over is at the midpoint of the line segment made by the frog who leaped, will a frog ever occupy the original empty vertex of the square?
    put the frogs on a coordinate plane so that the bottom left frogs coordinates are (0,0), top left frog’s coordinates are (0,1), and top right frog’s coordinates are (1,1). Observe that when a frog jumps, the parity of its coordinates is invariant therefore, none of the frogs can ever get to the bottom right corner, where the coordinates are (1, 0). Another way to say this is that none of the frogs have (odd, even) coordinates, and therefore, they can never land on an (odd, even) point
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