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THE HANOI TOWERS INSTALL
THE HANOI TOWERS SOFTWARE
THE HANOI TOWERS PLUS
THE HANOI TOWERS FREE

THE HANOI TOWERS INSTALL

George Dimitriadis, Montmorency Secondary College, has provided this Tower of Hanoi program (318Kb) for all to download, install and share. But you don't need to leap any further into the ether than right here.

THE HANOI TOWERS SOFTWARE

To use this task as a whole class investigation you could make use of the many software applets available on the Web which simulate the puzzle. Tasks can also be modified to become whole class investigations which model how a mathematician works. Whole Class Investigation Tasks are an invitation for two students to work like a mathematician.

However, Lucas was no doubt influenced by an older Hindu legend usually know as the Tower of Brahma. Euro-centric history records this puzzle as being invented by the French mathematician Edouard Lucas and being first marketed as a toy in 1883. To further extend the task include the time element suggested by the historic story. In this case that exponent is the number of discs. The graph of these pairs demonstrates exponential growth that is, growth governed by the exponent (or power) in the equation. discs produces a set of ordered pairs, ie: (No. Uncovering the number of moves for 1, 2, 3, 4. What would be the physical explanation from which this formula evolved? Of course the pattern could also be interpreted as 2 n - 1. This way of thinking is directly related to the sophisticated method of mathematical proof known as Mathematical Induction.

THE HANOI TOWERS PLUS

Then the previous tower can be shifted onto the translated base disc in the same number of moves as before.Ĭonsequently the students might interpret the sequence above as twice the previous number of moves plus one.

This reveals the new base which can be shifted in one move.

Moving the discs above the base disc is the same as moving the previous tower.

The next tower is the previous one atop a new base disc.

Assume the previous tower has been solved.

The other experience resulting from this approach may be to see that the moves for any tower, relate to the moves for the previous tower as follows: The number pattern that results from trying the simpler cases is 3, 7, 15, 31, 63 and so on which is very close to 4, 8, 16, 32, 64 and so on. This insight makes perfect sense once you have personal experience with attempting to solve the puzzle. Where you don't want the pile you put it if there is an even number. If you have an odd number you put the piece first where you want it. On the other hand, the legend told on the card suggests that other numbers of discs could be used, so why not apply the problem solving strategy of Try a simpler problem to see if the key movement patterns can be discovered and then applied to the problem on the card. Careful examination of each step in this way may lead to a solution. One way to approach this task is to consider options at each step and look ahead one move to see which is the better one. There is always more to a task than is recorded on the card. Iceberg A task is the tip of a learning iceberg.

reasoning strategies such as breaking a problem in to smaller parts.

A set of wooden discs in decreasing sizes.

You will find this in the whole class investigation section.

THE HANOI TOWERS FREE

In addition it has the equivalent of an investigation guide in the form of free Windows software created by George Dimitriadis which challenges your students to move any number of discs from 2-20. Other teachers have also provided ideas for efficiently and effectively making the equipment. This cameo has a From The Classroom section which shows how two teachers created a home made set of Tower of Hanoi puzzles from simple materials. Indeed, the powers of two pattern that appears out of the puzzle is what allows the task to be generalised as indicated in the story on the card. As students work with it however, they discover movement patterns and where there is a movement pattern, there will be a number pattern. The discs must be transferred from one spike to another without a larger disc every being on top of a smaller one. This classic logic task is a challenge at any level.