Explicit Rule
The explicit formula represents the minimum number of moves it takes to move n number of discs, calculated independently rather than based off the previous number of moves. The formula is T(n) = 2^n - 1, in which “n” represents the number of discs and ‘T(n)’ represents the minimum number of moves. For example, in order to complete the Tower of Hanoi with two discs you must plug 2 into the explicit formula as “n” and therefore, the minimum amount of moves using two discs is 3. The explicit formula is much easier to use because of its ability to calculate the minimum number of moves for even the greatest number of discs, or ‘n’. When solving the puzzle with 8 discs, by simply plugging in 8 for n it is easy to find that the minimum number of moves is 255 because it doesn’t rely on the number of moves for 7 discs. It is much more direct than the recursive, but it’s more difficult to play a higher level without first playing the level before it to discover the development of the pattern. The Tower of Hanoi is neither arithmetic nor geometric since neither addition nor multiplication patterns are present in the puzzle (mathforum).