MathDB

Along the direct highway Tmutarakan - Uryupinsk at points

A_1

A_2

\dots

A_ {100}

are the towers of the DPS mobile operator, and in points

B_1

B_2

\dots

B_ {100}

are the towers of the "Horn" company. (Tower numbering may not coincide with the order of their location along the highway.) Each tower operates at a distance of

10

km in both directions along the highway. It is known that

A_iA_k \geq B_iB_k

for any

i

k \leq 100

. Prove that the total length of all sections of the highway covered by the DPS network is not less than the length of the sections covered by the Horn network .

Problem Statement