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  1. The Towers of Hanoi

    If you are not familiar with the Towers of Hanoi puzzle, you should first read the legend and play the game. An explanation by Dr. Math can also be found in the 'Classic Problems' area of the Dr. Math FAQ.

    Creating a spreadsheet to model the Towers of Hanoi problem

    Start with a new ClarisWorks spreadsheet document and identify the headings you will need. For this example we will use the number of disks to be moved, the number of moves needed, and the time expressed in seconds, minutes, hours, days, weeks, and years. These have been abbreviated as follows.

    Because 1 disk can be moved from the left tower to the right tower with one move and each move takes one second, you can fill in the second row as follows:

    In the 3rd row you will enter the following formulas:

    Cell Formula Explanation
    A3 =A2 + 1 add one more disk for each row
    B3 =B2+1+B2 the previous number of moves plus one plus the previous number of moves (you need to move n-1 disks to the center post, then move the nth disk to the right post, then move n-1 disks to the right post)
    C3 =B3 the number of seconds is the same as the number of moves
    D3 =INT(C3/60) the number of minutes is the seconds divided by 60
    E3 =INT(D3/60) the number of hours is the minutes divided by 60
    F3 =INT(E3/24) the number of days is the hours divided by 24
    G3 =INT(F3/7) the number of weeks is the number of days divided by 7
    H3 =INT(F3/365.25) the number of years is the number of days divided by 365.25

    In columns D through H the "INT" function us used so that all answers appear as whole number values.

    Now highlight the 3rd row and drag down to highlight the rows through the 65th row. With these cells highlighted choose "fill down" from the Calculate menu.

    While these cells are still highlighted choose "number" from the Format menu. For this problem we will choose Fixed with precision 0 and commas.

    We also need to adjust the column width to 150; this can be done by choosing column width from the Format menu.

    You could now look at the data in a graph. Highlight cells A1 through B10. Choose "Make a Chart" from under the Option Menu. Choose x-y line and click OK.

  2. Timber

    A lumber company owns 7000 birch trees. Each year the company plans to harvest 12 percent of its trees and plant 600 new ones. How many trees will the company have after 3 years? Do you see a long-term trend?

  3. Cookies and Cream

    The Polar Bear Ice Cream Company has a monthly revenue of $10,000 for its Cookies and Cream ice cream. Its competitor, the Royal Ice Cream Company, sells a similar flavor of ice cream from which it realizes a monthly revenue of $7,000.

    Each month some customers change brands; however, the total amount of money that is available to spend on Cookies and Cream ice cream is always a constant $17,000. Suppose that 80% of the customers stay with their current brand and 20% switch. What will the distribution of income be after 6 months? Predict the long-term distribution of income for the two companies.

  4. Hypertension

    To help control hypertension, a person takes a tablet containing 25 milligrams of a drug each morning. During the next 24 hours, 20 percent of the drug in the body is eliminated. What will be the level of the drug in the person's body after 10 days? Predict the level that the drug will eventually accumulate in the person's body.

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