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Unformatted text preview: number of move required(optimally) to reach the goal is: T n = 2 T n-1 + 1 , where T 1 = 1. Ti = number of moves required to place total i disk properly. Supppse the pegs are A,B & C.To move n disks from peg A to peg C: 1 move n?1 disks from A to B. This leaves Dn on peg A 1/2 2 move Dn from A to C 3 move n?1 disks from B to C so they sit on Dn If we solve this recursive equation then we will get the number of move is 2 n-1. c. What is the total number of legal states? Let, the disks, Dn, Dn-1 , . .. D1 are indexed according to their size. So Dn is the largest and D1 is the smallest. The possible choice for putting Dn in peg is 3. For each of the mentioned option of Dn, the option for D n-1 is 3. In this way we can say that number of legal moves is, 3* 3 * . .. * 3 = 3 n 2/2...
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- Spring '11