MathDB
max no of several identical matches (2022 Novosibirsk Oral Geo Oly 7.7)

Source:

September 2, 2023
geometrycombinatorial geometrycombinatorics

Problem Statement

Vera has several identical matches, from which she makes a triangle. Vera wants any two sides of this triangle to differ in length by at least 1010 matches, but it turned out that it is impossible to add such a triangle from the available matches (it is impossible to leave extra matches). What is the maximum number of matches Vera can have?