| Tower Of Hanoi (report) | ||||||||||||||||||||||||
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Introduction The French mathematician, Edouard Lucas invented the Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle), in 1883. When French mathematician he invented the world-renowned Tower of Hanoi, he surely didn't envision that children's game could help aspiring computer scientists a century later understand the mechanics of programming. Partly named after one of the centers of France's late 19th- century empire in Indochina, the puzzle consists of three posts. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might have been used for the mental discipline of young priests. Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important proviso-a large disk could never be placed on top of a smaller one. The priests worked very efficiently, day and night. When they finished their work, the myth said, the temple would crumble into dust and the world would vanish. Objectives Our group's objectives are to do a very good webpage on the Tower Of Hanoi and get the gold award. We will achieve this by collecting information, doing some investigations and getting ideas from all the sources so as to do an outstanding webpage. Doing an outstanding webpage is difficult, but clinching the gold award is even more difficult. But, we will always try to do a webpage that is very good and get the gold award for it. Now, our group has put in a lot of effort in doing the webpage. But, it is the judge's final decision that proves that whether the webpage that we had done is an excellent one or just a normal one. Our group's another aim is to attract lots of people to visit our webpage so that the webpage will be popular and these will achieve our aim. Right now, I had ask our classmates to visit our webpage and give us their opinion so that we could improve our webpage but some of them are busy with their own projects and had no time to visit our webpage. Our last objective is to find the method which could solve the Tower Of Hanoi game. So far, we had already found the method for solving the Tower Of Hanoi. In conclusion, we hope to achieve our objectives. Method A stack of disks is arranged in increasing order of size from top to bottom on one of the posts. Under traditional rules, a player must move the stack, one disk at a time, from one post to another without ever placing a larger disk on top of a smaller disk. The difficulty of the puzzle largely hinges on the number of disks in the stack. The Tower of Hanoi is an interesting game. We have done three exercises on it and I will take one to show the methods and findings. There is a question on a farmer who wants to bring his cat, parrot and carrots over the river. He can only bring one at a time but he knows that the cat will eat the parrot and the parrot will eat the carrots if he is not around. Therefore, we are suppose to help the farmer find a solution to this problem. Solution: The farmer first brings the parrot across and return. Then, he brings the carrots across, returning with the parrot. He leaves the parrot at the bank again and brings the cat over. Finally, he returns and brings the parrot across. We found out that this question can be related to our project-Tower of Hanoi. Like the above exercise, The Tower of Hanoi also has three disks which you need to move it from the first peg to the last peg. In the case of that the cat will eat the parrot and the parrot will eat the carrots, it is similar to the rule that you are not supposed to put a larger disk on a smaller one. We also need to know where we should transfer the disks to. If we transfer the disk to the wrong peg, we will need more moves to complete the game. We also found out this solution below-to find the minimum number of moves to complete the game required for each disk. Firstly, we have to find out the minimum number of moves for three disks, which is seven. Number of disks Minimum moves required to complete the game 3456 7??? If we find the minimum number of moves for four disks, which is 15, we will find that there is a relationship between seven and fifteen. Therefore, I can make a theory here that the minimum number of moves required is 2n+1, whereby n= the previous minimum moves required. From here, I can conclude that minimum moves required for 5 disks is = 2n+1= 2x15+1=31 Our information are from:www.mazeworks.com www.math.toronto.edu/mathnet/games/towers.html www.math.toronto.edu/mathnet/games/towers.html www.rainfrog.com/games/towers.shtml By:Toh Yean Lih(leader)1N-26 Koo Zhi Xuan1N-09 Wang Bang Zhi(PRESENTER)1N-29 | |||||||||||||||||||||||
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