The rotation rule entails aggregating all values and computing the modulus with respect to 'n.' For instance, if 'n' is 6 and the values are (1,3), (1,2), and (1,5), the resultant sum (3+2+5) mod n equals 4, signifying that the rotations can be represented as (1,4). Conversely, the flip rule involves adding values with alternating signs. For example, with values (2,3), (2,1), (2,5), and (2,4), the sum (-3) + 1 + (-5) + 4 equals -3, and when considering the modulus with 'n,' it becomes +3. This aligns with the concept that the sum of all rotations signifies the number of rotations from the initial state. Additionally, the requirement for the total number of flips to be even ensures that the positions do not become mirror images of the initial state.