Page 27 - NUMINO Challenge_D1
P. 27
3 Magic Square
Basic Concepts Magic Square
Magic Square is an arrangement in which the sums of
numbers in each row, column, and diagonal are equal.
About 4000 years ago, a special turtle was found near a
majestic waterfall in ancient China. The dots on its shell
formed a magic square. This story is the oldest known
record of the magic square, and since then people have been fascinated
by the magic square and its properties.
Example Use numbers from 1 to 9 without repetition, so that
all the sums of the numbers in each row, column,
and diagonal are equal.
Class Notes .
The sum of three numbers in each row is (the sum of numbers from 1 to 9) 3
There are 4 lines that pass through the middle cell. The sum of numbers in these 4 lines is
(the sum of the three numbers in each line) 4 4.
The number in the middle cell is added 4 times, and the numbers in
each of the remaining eight cells are added once. Therefore, the sum of
numbers in these 4 lines is equal to the sum of numbers from 1 to 9 plus
the number in
the middle cell added times.
Let' s use to represent the number in the middle cell. The sum of numbers in the
4 lines is (1 2 3 8 9) ..
There are two ways to place 9 in the magic square, as
shown on the right. Since the magic square on the 9 9
immediate right cannot be completed, fill in the magic
square on the far right so that the sum of the three
numbers in each row and column is .
24 NUMINO Challenge D1
Basic Concepts Magic Square
Magic Square is an arrangement in which the sums of
numbers in each row, column, and diagonal are equal.
About 4000 years ago, a special turtle was found near a
majestic waterfall in ancient China. The dots on its shell
formed a magic square. This story is the oldest known
record of the magic square, and since then people have been fascinated
by the magic square and its properties.
Example Use numbers from 1 to 9 without repetition, so that
all the sums of the numbers in each row, column,
and diagonal are equal.
Class Notes .
The sum of three numbers in each row is (the sum of numbers from 1 to 9) 3
There are 4 lines that pass through the middle cell. The sum of numbers in these 4 lines is
(the sum of the three numbers in each line) 4 4.
The number in the middle cell is added 4 times, and the numbers in
each of the remaining eight cells are added once. Therefore, the sum of
numbers in these 4 lines is equal to the sum of numbers from 1 to 9 plus
the number in
the middle cell added times.
Let' s use to represent the number in the middle cell. The sum of numbers in the
4 lines is (1 2 3 8 9) ..
There are two ways to place 9 in the magic square, as
shown on the right. Since the magic square on the 9 9
immediate right cannot be completed, fill in the magic
square on the far right so that the sum of the three
numbers in each row and column is .
24 NUMINO Challenge D1
