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How to Create a Magic Square of City Populations in Excel

The magic square is a grid of seemingly random numbers in which the sum of the rows, columns and diagonals is the same. Normal magic squares, in which whole numbers are used and the number of rows and columns are equal, are solved by a simple algebraic equation: the sum of each row = [the number of columns( number of rows ^2 + 1)]/2. Using a spreadsheet program such as Microsoft Excel, you can create an abnormal magic square for any number. Abnormal squares may have decimals and negative numbers, so they are time-consuming to solve with pen and paper but make fun demonstration pieces. For example, you could use a magic square to introduce a geography unit on population control.

Instructions

    • 1

      Open Excel by clicking "Start" and typing "Excel" into the search bar. Left-click the program name to launch it.

    • 2

      Click "Ctrl" and "S" simultaneously to save the workbook. Give the file an appropriate name such as "Magic Square City Pop."

    • 3

      Click on cell A3. Press "Ctrl" and the tilde key, located to the left of the "1" key, to activate the formula view.

    • 4

      Fill in column A, rows 3 through 7 with the following formulas: =(E1-34)/4+1, =1+C5, =1+C4, =1+A4, =Sum(A3:A6).

    • 5

      Fill in column B, rows 3 through 7 with the following formulas: =1+C3, =1+D5, =1+D4, =1+C6, =Sum(B3:B6).

    • 6

      Fill in column C, rows 3 through 7 with the following formulas: =1+A6, =1+B4, =1+B5, =1+A3, =Sum(C3:C6).

    • 7

      Fill in column D, rows 3 through 7 with the following formulas: =1+B6, =1+A5, =1+D3, =1+B3, =Sum(D3:D6).

    • 8

      Type "City Population" in cell D1.

    • 9

      Fill in column E, rows 3 through 7 with the following formulas: =Sum(A3:D3), =Sum(A4:D4), =Sum(A5:D5), =Sum(A6:D6), =+D6+C5+B4+A3.

    • 10

      Press "Ctrl" and tilde simultaneously to return to normal view. Type a city population into cell E1; the formulas will automatically fill in the magic square.

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