MathDB

9

Part of 2016 Latvia Baltic Way TST

Problems(1)

partition 1 to 2016 into 3 subsets, a+ b=c

Source: 2016 Latvia BW TST P9

12/17/2022
The numbers from1 1 to 20162016 are divided into three (disjoint) subsets A,BA, B and CC, each one contains exactly 672672 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.
combinatoricsSubsets