Prime 15 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 post Share on other sites

0 Solution witzar 18 Posted February 8, 2013 Solution 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 post Share on other sites

0 Prime 15 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 post Share on other sites

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## Prime 15

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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