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Three frogs are placed on three vertices of a square. Every minute, one frog leaps over...

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Advance Math

Three frogs are placed on three vertices of a square. Everyminute, one frog leaps over another frog, in such a way that the"leapee" is at the midpoint of the line segment whose endpoints arethe starting and ending positions of the "leaper". Will a frog everoccupy the vertex of the square which was originallyunoccupied?

Answer & Explanation Solved by verified expert
3.9 Ratings (358 Votes)
Let us develop some terminology to help us better understand theproblemWe will say that the coordinate pair is a latticepoint if both and are integersFor example is a latticepoint while is notLet us suppose we have a unit square with vertices and Without loss of generality let us assume that the three frogsare at the vertices and respectivelyIf not we can always rotate the square to do soAnother terminology being even and beingodd observe that and    See Answer
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