partition 1 to 2016 into 3 subsets, a+ b=c
Source: 2016 Latvia BW TST P9
December 17, 2022
combinatoricsSubsets
Problem Statement
The numbers from to are divided into three (disjoint) subsets and , each one contains exactly numbers. Prove that you can find three numbers, each from a different subset, such that the sum of two of them is equal to the third.[hide=original wording]Skaitļi no 1 līdz 2016 ir sadalīti trīs (nešķeļošās) apakškopās A, B un C, katranotām satur tieši 672 skaitļus. Pierādīt, ka var atrast trīs tādus skaitļus, katru no citas apakškopas, ka divu no tiem summa ir vienāda ar trešo.