If you did not have a strategy yet, do not give up! See if you can find a pattern now.If you had a strategy, can you extend it to the five-disk tower? Challenge yourself and try the five-disk tower.Do you have a strategy? Could you explain to a friend how you finish the game?
Play the game a few more times and observe closely.Can you find a way to do it in as few moves as possible? Does anything you learned while solving the three-disk tower help you solve the four-disk one? Can you finish the game with fewer moves? Do you think you can finish the game with the smallest possible number of moves? Stack three disks (from largest to smallest) on the leftmost square and start over. Once you master the two-disk tower, try with three disks.Do you think you can find the “best” solution, with the smallest possible number of moves? Replay the game with the two-disk tower.Can you move the tower to the rightmost square, following the rules above? How many moves did you need? If you get confused or cannot finish the game, ask a friend to help you. Try the game with your two-disk tower.Looking at the rules, can you see it is not allowed to place a disk off the board? Where does it state you cannot start two towers on one square?.Disks can be placed on an empty square on the board or on a larger disk, but disks cannot be placed next to each other on top of a larger disk. You can only move the topmost disk from any square. The goal of the game is to move the tower to the rightmost square of the board while following these rules: The starting position of the game is a tower on the leftmost square of the board (like the two-disk tower you have now).Stack them on the leftmost square of your cardboard, with the smaller disk on top of the larger disk. Start the game with your two smallest disks.Draw two straight lines to divide the cardboard into three equal-size squares (about five by five inches each).Five different-size disks such as buttons, bottle caps, container lids, etcetera (The biggest disk needs to have a diameter no larger than five inches.).Don’t worry! Play the game, and you might realize that you develop these “solutions” on your own. These terms might seem hard to understand. Patterns and translating these in mathematical formulas. Recursive solutions, where you use information from one step to find the next step Iterative solutions, where the same sequence of instructions is repeated over and over If you try to explain how you solve the puzzle, you might realize you use one of the following mathematical concepts: As you play the game with more and more disks, you will notice you start to look for patterns. You might wonder how mathematics is involved in playing this game. That is more than 40 times the age of the universe! Using mathematics, you can calculate that even when the priests found the most efficient way to solve the problem, and moved the disks at a rate of one per second, it would take almost 585 billion years to finish the job. The priests' goal was to re-create the stack on a different post by moving disks, one at a time, to another post with the rule that a larger disk could never be placed on top of a smaller disk. Each disk rested on a slightly larger disk. In the legend the young priests were given 64 gold disks stacked neatly on one of three posts. It is associated with a legend of a Hindu temple where the puzzle was supposedly used to increase the mental discipline of young priests. The tower of Hanoi (also called the tower of Brahma or the Lucas tower) was invented by a French mathematician Édouard Lucas in the 19th century. But math can also be used for entertainment-mathematical games, riddles, challenges and puzzles are also interwoven throughout history! Throughout history mathematics has fulfilled many practical needs such as measuring plots of land, studying astronomy and calculating taxes. People have been playing these games and puzzles for centuries! They are fun, entertaining and sometimes useful. Think about simple games such as tic-tac-toe, more strategic games such as chess or math puzzles such as sudoku. Are you tired of math work sheets and homework? Did you know that there are more creative ways to exercise your mathematical muscle? A lot of games, puzzles and riddles revolve around mathematical concepts.