Question 31
Twenty integers are written around a circle.
For each of them, the sum of the $10$ numbers that follow it in the clockwise direction is computed. When this is done, each of the $20$ numbers is replaced by its corresponding sum.
Prove that after repeating this process several times, each of the $20$ numbers around the circle will be even.
For each of them, the sum of the $10$ numbers that follow it in the clockwise direction is computed. When this is done, each of the $20$ numbers is replaced by its corresponding sum.
Prove that after repeating this process several times, each of the $20$ numbers around the circle will be even.