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5 numbers wanted, 10 sums given May Olympiad (Olimpiada de Mayo) 2013 L1 P4

Source:

September 29, 2021
algebra

Problem Statement

Pablo wrote 55 numbers on one sheet and then wrote the numbers 6,7,8,8,9,9,10,10,116,7,8,8,9,9,10,10,11 and 12 12 on another sheet that he gave Sofia, indicating that those numbers are the possible sums of two of the numbers that he had hidden. Decide if with this information Sofia can determine the five numbers Pablo wrote .