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Making a Magic Square
Mathematical - logical activity in Gimnazjum nr3 Mylenice,
Poland
Some properties:
Magic number is 30
3+6+7+9+10+11+13+14+17 = 90
90:3=30
30:3 =10 the number in the middle
10= +
=
+
=
+
=
+
7 = +
, 14=
+
, 6 =
+
, 13 =
+
+ + =336 = ++
+ + = 374 =+ +
Create magic square from the number : 1,3, 5, 7, 9, 11, 13, 15,
17 using this
properties.
1+3+5+7+9+11+13+15+17=81
81:3=27 magic number
27 :3= 9 number in the middle
7 9 14
17 10 3
6 11 13
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You can notice that in this magic square are working 3 numbers
9, 6, 2:
We can try make own magic square using 3 number in such way,
for example 5, 3, 1
7 5 15
17 9 1
3 13 11
9-2 9-6+2 9+6
9+6+2 9 9-6-2
9-6 9+6-2 9+2
5-1 5-3+1 5+3
5+3+1 5 5-3-1
5-3 5+3-1 5+1
4 3 8
9 5 1
2 7 6
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So we have magic square , the magic number is 15.
Benjamin Franklin, a former president of the USA, discovered a
way of
creating a magic square for any chosen magic number.
He did this by using algebra, whereby you choose values for a, b
and c,
then substitute them into the formulas shown in the grid.
Fill in the correct numbers in the Magic Square, for the given
values of a,
b and c.
1) a = 6, b = 4, c = 1 2) a = 10, b = 6, c = 2
Magic Number = Magic Number =
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3) a = 12, b = 10, c = 5 4) a = 25, b = 25, c = 6
Magic Number = Magic Number =
Can you see the link between the magic number and a, b or c?
Making a Magic Square (your own ones!)
Fill in the correct numbers in the Magic Square, for the given
values of a, b and
c.
1) a = , b = , c = 2) a = , b = , c =
Magic Number = Magic Number =
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Why does this work?
Imagine we added up the rows and columns using the algebra
instead of
numbers:
a-c+a-b+c+a+b = 3a
In every row, column and diagonal, the Algebra adds up to 3a
So they will all be the same number
The middle number multiplied by 3!
Multiply every number of magic square by 2
Is it Magic square? Yes , magic number is 30.
4 3 8
9 5 1
2 7 6
8 6 16
18 10 2
4 14 12
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Add two of this magic squares
+
=
12 9 24
27 15 3
6 21 18
You have next magic square. What is the magic number ? 45 = 15
+30
4 3 8
9 5 1
2 7 6
8 6 16
18 10 2
4 14 12
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Tasks for our partners:
Use your math skills to fill in each in these magic squares.
1.
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2.
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3.
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4.
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5.
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6.
Good luck !!!
