Magic Square 24

Magic Square 4×4 (Photo credit: Wikipedia)

Magic Squares: Even

Do you know what a magic square is?

It is a grid of numbers that add up to the same number whether you add up all the numbers across a row, or down a column, or diagonally.

You can make your own.

Let’s start with an even number of columns and rows in the square.

We will make one with 4 rows and 4 columns, a grid design that is also described as 4×4 (four by four).

Materials:

  • Paper
  • Pens or pencils
  • Ruler or straight edge

Instructions:

  • Draw a grid that has four rows and four columns.
  • Put numbers in each square of the grid, starting with 1 in the upper left-hand corner of the grid.
  • The first time, write in numbers only in the corner squares and the middle squares, that is, only those squares on the diagonal, but keep counting as though you were writing them all in.
  • That is, for a 4×4 grid, write 1 in the top left corner, skip (but count in your head, 2, 3) the next two squares along the top row and write 4 in the upper right corner.
  • Continue on the next row, again starting on the left edge, (count 5 in your head, but don’t write it in the square), then write 6 in the left middle square and 7 to the right of it.
  • When you are done, start counting over from 16 down to 1, again at the top left corner. Only write numbers in the blank squares, but count every square.
  • Thus, counting the top left square as 16, skip it because it already has a one in in, then put 15 in the square to the right of it, and 14 to the square to the right of that
  • Skip the square that already has 4 in it, start on the second row, on the left most square and put 12 in it, then skip the squares that already have 6 and 7 in them (counting 11, 10) and put 9 in the right-most square in the second row.
  • This should work for any magic square divisible by 4, that is 4×4, 16×16, 64×64
  • Thanks to mathforum.org for this explanation.

What Should Happen?

  • You should have a square that reads on the top row, 1, 15, 14, 4.
  • On rhe second row, it should read, from left to right, 12, 6, 7, 9.
  • On the third row, it should read, from left to right, 8, 10, 11, 5.
  • And, on the fourth row, it should read, from left to right, 13, 3, 2, 16.

Every row and column and the diagonals should add up to the same number, 34.

How Is This Useful?

Magic squares can be used in round-robin tournament scheduling. 

For example, the numbers in the first column may represent four teams that are playing in a three-week tournament.

The next column represents who that team will play in Week 1, the third column who they will play in Week 2 and the fourth column who they will play in Week 3.

Similarly, magic squares can be used in experimental drug design.

If a scientist wanted each of four participants to take four different drugs, but not at the same time, they could lay out the schedule with a magic square.

Thanks to drmikesmathgamesforkids.com for this activity.

 

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers

http://newgrandmas.com

 

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