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ASU 350 All Soviet Union MO1983 3 numbers, blackboard {17, 1967, 1983}

Source:

July 28, 2019
number theorycombinatoricsgame strategyblackboard

Problem Statement

Three numbers were written with a chalk on the blackboard. The following operation was repeated several times: One of the numbers was cleared and the sum of two other numbers, decreased by 11, was written instead of it. The final set of numbers is {17,1967,1983}\{17, 1967, 1983\}.Is it possible to admit that the initial numbers were
a) {2,2,2}\{2, 2, 2\}?
b) {3,3,3}\{3, 3, 3\}?
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