Tower of Hanoi 4 peg « Math World

Tower of Hanoi 4 peg

In class on Sept. 30, 2008, we had an interesting session. Elise and Adam lead the class with their recursive patterns for solving the 4 peg system. The concept was that a 3 peg sytem can be used to give the answer for the minimal amount of moves needed to solve a 4 peg system. Elise came up with a mathematical calculation process to attain the least amount of moves.

{Let P denote the number of pegs and let the number of disks be at least $1 + \sum_i^{P-1}i$ . We attempted to formulate a function $\psi (P, P-k)$ . P in the function denotes the number of available pegs. P-k denotes the number of disks moved. found that the opening moves would always be $\psi(P, P-1), \psi(P-1, P-2), \psi(P-2, P-3),...,\psi(2 , 1)$ Let A denote the first parameter in the function and B denote the second. Then, the function $\psi$ evaluates to the least number of moves to move B disks with A available pegs. The function $\psi$ can be viewed as a sequence which ends when there are no more empty pegs.} from elise blog….