BrainDen.com - Brain Teasers
• 0

# 1966

Go to solution Solved by witzar,

## Question

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.

## Recommended Posts

• 0
• Solution

The operation decreases the sum of all numbers by even number, but (1+2+...+1966) is odd.

##### Share on other sites
• 0

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.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.