Introduction$-$to$-$Artificial$-$Intelligence$-$

Homework$-1$

$1$ Towers of Hanoi

The$-$Towers of Hanoi$-$is a famous problem for studying recursion in computer science and recurrence equations

and two empty pegs.$\text{'}$We are allowed to move a disc from one peg to another, but we are never allowed to move

a$.$larger $-$disc $-$on top of a smaller$-$disc.$\text{'}$ The$-$goal is to move all the discs to the rightmost peg $($see the figure above$).$

$($a$)$ Propose a a state representation for the problem.

$($b$)$ What is the size of the state space?

$($c$)$ What $*$ is the start'state?

$($d$)$ From$-$a given state, what actions are legal?

$($e$)$ What is the goal test?