Pt1420 Unit 7 Lab Report Conclusion

Conclusion There were two main goals of this investigation. The first one was to find an equation that would produce the perfect number of moves for any number of disks that are being used in the puzzle. The second goal was to find a pattern between all of the different number of disk puzzles. The first goal of finding an equation was accomplished through trial, error, and logical thinking. By first graphing the data points, many equation types were able to be eliminated and a focus was put on exponential equations until the equation that worked perfectly with the data was found. The second goal was also accomplished in a similar manner. When there was not a clear correlation between the 3 disk puzzle and the 4 disk puzzle, the 5 disk puzzle

The first 7 moves and the last 7 moves of the 5 disk puzzle are the same as solving the 3 disk puzzle. This means that the 7 disk puzzle will start with the same 31 moves for the 5 disk puzzle and the same 31 moves to finish the 7 disk puzzle. The 6 disk puzzle was also completed but there are not any pictures or commentary in this investigation. The 6 disk puzzle showed that the first 15 moves and the last 15 moves of the 6 disk puzzle are the same as solving the 4 disk puzzle. This shows that the odd number disk puzzles have the same pattern and the even number disk puzzles have the same pattern. This means that if the player knows how to solve the previous odd or even number puzzle, they can solve the beginning and end of the next odd or even number puzzle perfectly. Overall, the two goals are going to make solving this brain

The first goal of this internal assessment was to find an equation that would help to calculate the perfect number of moves for each puzzle no matter how many disks were being used. By testing how different function lines matched up with the three base points, there was a clear correlation and an equation was easily found. After the first goal was met, the second goal of this internal assessment was put into action. The second goal of identifying a pattern or algorithm to perfectly solve each puzzle every time was a more difficult challenge. Now that there is an equation for the number of moves and a recognizable pattern between the odd numbered disks and the even numbered disks, the goals of this internal assessment have been met. In the introduction, the story behind the Tower of Hanoi was explained. The story involved the 64 golden disks and the end of the world. If these disks existed, it would be interesting to see how moves it would take to be completed. When plugged into the function (y=264-1), the total number of moves was 18,446,744,073,709,551,615. Now that is an impressive number. This application was a fun twist on the original goals of this