MathDB

6

Part of 2005 Junior Tuymaada Olympiad

Problems(1)

comparing mobile networks' length coverage

Source: Tuymaada Junior 2005 p6

5/12/2019
Along the direct highway Tmutarakan - Uryupinsk at points A1 A_1 , A2 A_2 , … \dots , A100 A_ {100} are the towers of the DPS mobile operator, and in points B1 B_1 , B2 B_2 , … \dots , B100 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 1010 km in both directions along the highway. It is known that AiAk≥BiBk A_iA_k \geq B_iB_k for any i i , k≤100 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 .
combinatorics