6. 2017 numbers are written. It is known that the sum of the squares of any 7 of them is 7, the sum of any 11 of them is positive, and the sum of all 2017 numbers is divisible by 9. Find these numbers.
Answer: Five numbers are equal to -1, the rest are equal to 1.

Solutions: The sum of the squares of any 7 numbers is equal to 7. Therefore, all these squares are equal to 1. All these numbers are equal to +/-1. The sum of 11 is positive, which means the number of -1 does not exceed 5. If all are equal to 1, then the sum is 2017, which is not divisible by 9. If we change the sign of one unit - the sum will decrease by 2. Doing this 5 times will result in 2007, which is divisible by 9.