Question 32
Each space on a $3 \times 3$ board contains a light button that can be on or off. Pressing the center button changes the status of his eight neighbors but not himself. Pressing any other button changes its state and that of each neighboring button.
Pressing a button is counted as one step.
Two configurations are connected if they can be passed from one to the other in a finite number of steps.
Distance between two connected configurations is defined as the minimum number of steps that are necessary to move from one to the other.
Determine the maximum distance that can be between two connected configurations.
Pressing a button is counted as one step.
Two configurations are connected if they can be passed from one to the other in a finite number of steps.
Distance between two connected configurations is defined as the minimum number of steps that are necessary to move from one to the other.
Determine the maximum distance that can be between two connected configurations.