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# Magic Squares

#### You will need to be able to:

• perform the basic spreadsheet skills

#### Language used:

 toolbar standard toolbar functions sigma sum summation

• Enter the numbers 1 to 9 in any order into the cell range A2:C4. This region is shown shaded in the diagram below.
• Select A5, then write the formula = A2+A3+A4
which will add together the contents of cells A2, A3 and A4.
• Move to cell D2 and add the contents of A2, B2 and C2.

 A B C D 1 2 3 4 5

The standard toolbar, as shown at the bottom of this page, allows you to use the mouse to directly select some useful functions.

• Select cell B5, then press the S button on the standard toolbar. A formula appears

= SUM(B2:B4)

• The cells B2, B3 and B4 are highlighted with a moving dashed line.
1. What happens when you press return?

2. What does this do?

3. What is the name of the symbol  ?

• Select C5 then write the formula

=SUM(C2:C4)
taking careful note of what happens when you type in the second bracket.

• Press return.

This is a different way of entering the same summation formula.

1. What happened when you typed in the second bracket?

• Select D4 then type =SUM(
• Select A4 then drag across to C
• Press return.
1. What happens?

You will need to type in the final bracket and press return.

### Introductory Investigation

1. What happens if you interchange one or more of the numbers in the cells A2:C4?

2. What happens if you change the numbers to the arrangement shown below?

 6 7 2 1 5 9 8 3 4

• Enter a formula into D5 to find the sum of cells A2, B3 and C4.
• Enter a formula to do the same along the other diagonal.
1. What do you notice?

This is known as a magic square.

### Further Investigation

Try to construct a 5 x 5 magic square using the numbers 1 to 25. The rows, columns and diagonals should add to 65. Make a copy of your completed square.

Try to construct a 4 x 4 magic square with rows, columns and diagonals summing to 34.

#### You should now know how to:

• calculate sums using at least two different methods
• recognise the standard toolbar and use the  function button.
• construct and define a magic square.