Prime 15 Report post 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.) Share this post Link to post Share on other sites

0 witzar 18 Report post Posted February 8, 2013 The operation decreases the sum of all numbers by even number, but (1+2+...+1966) is odd. 1 Share this post Link to post Share on other sites

0 Prime 15 Report post 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. Share this post Link to post Share on other sites

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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