Prime Posted February 8, 2013 Report Share Posted February 8, 2013 All numbers from 1 to 1966 are written on a blackboard. You are allowed to erase any two numbers and write their difference instead. Prove that repetition of that operation may not result in having only zeroes on the blackboard. (Problem from Russian Math Olympiads. 6-th grade, 1966.) Quote Link to comment Share on other sites More sharing options...
0 witzar Posted February 8, 2013 Report Share Posted February 8, 2013 The operation decreases the sum of all numbers by even number, but (1+2+...+1966) is odd. 1 Quote Link to comment Share on other sites More sharing options...
0 Prime Posted February 8, 2013 Author Report Share Posted February 8, 2013 The operation decreases the sum of all numbers by even number, but (1+2+...+1966) is odd. Nice. When at math competition, solve it like this and you have extra time to tackle other problems. Quote Link to comment Share on other sites More sharing options...
Question
Prime
All numbers from 1 to 1966 are written on a blackboard.
You are allowed to erase any two numbers and write their difference instead.
Prove that repetition of that operation may not result in having only zeroes on the blackboard.
(Problem from Russian Math Olympiads. 6-th grade, 1966.)
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