Question 56
We have a row of 203 squares. Initially the leftmost square contains 203 chips, and the others are empty. In each move we can perform one of these two operations:
* Take one chip and move it to an adjacent square (to the left or to the right).
* Take exactly 20 chips from the same square and move them all to an adjacent square (all to the left or all to the right).
After 2023 moves, each square contains one chip. Prove that there is a chip that has been moved to the left at least nine times.
* Take one chip and move it to an adjacent square (to the left or to the right).
* Take exactly 20 chips from the same square and move them all to an adjacent square (all to the left or all to the right).
After 2023 moves, each square contains one chip. Prove that there is a chip that has been moved to the left at least nine times.