Recursive Rule
The recursive formula represents the sequence for the minimum number of moves it takes to move n number of discs based on the previous number of moves. The formula is T(n) = 2(tn-1) + 1, T(1) = 1, in which n represents the number of discs, T(n) represents the minimum number of moves, and (tn-1) represents the previous number of moves. For example, in order to complete the Tower of Hanoi with two discs you must plug 1 in as tn-1 because 1 is the minimum number of moves it takes to complete the game with one disc (the previous number of discs). Using two discs, the minimum number of moves to completing the puzzle is 3. Continue plugging in numbers for ‘n’ in order to find the next minimum number of moves possible to complete the level most successfully (mathforum). The recursive formula is practical because you have to pass one level before you can get to the next; otherwise, you won’t know the pattern as the number of discs increases by one more. By calculating and solving the puzzle in the minimum number of moves, you can then find in how many moves the next number of discs can be completed.