Same multisets of sums
Source: Kyiv City MO 2022 Round 1, Problem 11.1
January 23, 2022
algebra
Problem Statement
The teacher wrote distinct real numbers on the board. After this, Petryk calculated the sums of each pair of these numbers and wrote them on the left part of the board, and Vasyl calculated the sums of each triple of these numbers and wrote them on the left part of the board (each of them wrote numbers). Could the multisets of numbers written by Petryk and Vasyl be identical?