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Graph problem that is given as a graph problem, unusual

Source: Saint Petersburg MO 2020 Grade 9 Problem 7

May 7, 2020
combinatorics

Problem Statement

Let GG be a graph with 400400 vertices. For any edge ABAB we call a cuttlefish the set of all edges from AA and BB (including ABAB). Each edge of the graph is assigned a value of 11 or −1-1. It is known that the sum of edges at any cuttlefish is greater than or equal to 11. Prove that the sum of the numbers at all edges is at least −104-10^4.
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