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Frog jumping on points on a plane

Source: India Postals 2015 Set 1

November 7, 2015

combinatorics

Problem Statement

For each point

X

in the plane, a real number

r_X > 0

is assigned such that

2|r_X - r_Y | \le |XY |

, for any two points

X, Y

. (Here

|XY |

denotes the distance between

X

and

Y

) A frog can jump from

X

to

Y

if

r_X = |XY |

. Show that for any two points

X

and

Y

, the frog can jump from

X

to

Y

in a finite number of steps.

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