Page 31 - NUMINO Challenge_D1
P. 31
Type 3-2 Multiplication Magic Square
Use numbers 1, 2, 3, 4, 6, 9, 12, 18, and 36, without
repetition, to fill in the square, so that the products of the
three numbers in each row, column, and diagonal are
equal.
1 Since the products of the three numbers in each row,
column, and diagonal are equal, the products of all pairs of
numbers besides the number in the middle cell, need to be
equal. Circle the number that will go in the middle cell and
pair the eight remaining numbers so that their products are equal.
1 2 3 4 6 9 12 18 36
2 There are two cases in which the numbers 36 and 1 can be placed
differently. In , the multiplication magic square cannot be made. Fill in
the blanks and complete the magic square in .
Since 6 is the only number that can be placed in the middle cell,
1 the product of the three numbers in each straight line is 216.
Therefore, should be 6, and each value of and can
36 be either 2 or 3. When 2, should be 108. When 3,
should be 72. Therefore, the magic square cannot be
completed.
Since is the only number that can be placed in the middle cell,
1
the product of the three numbers in each straight line is .
36 Therefore, the two numbers that are in the same line as 36 are
and . The product of these two numbers is 6.
The two numbers in the same line as 1 are and .
28 NUMINO Challenge D1
Use numbers 1, 2, 3, 4, 6, 9, 12, 18, and 36, without
repetition, to fill in the square, so that the products of the
three numbers in each row, column, and diagonal are
equal.
1 Since the products of the three numbers in each row,
column, and diagonal are equal, the products of all pairs of
numbers besides the number in the middle cell, need to be
equal. Circle the number that will go in the middle cell and
pair the eight remaining numbers so that their products are equal.
1 2 3 4 6 9 12 18 36
2 There are two cases in which the numbers 36 and 1 can be placed
differently. In , the multiplication magic square cannot be made. Fill in
the blanks and complete the magic square in .
Since 6 is the only number that can be placed in the middle cell,
1 the product of the three numbers in each straight line is 216.
Therefore, should be 6, and each value of and can
36 be either 2 or 3. When 2, should be 108. When 3,
should be 72. Therefore, the magic square cannot be
completed.
Since is the only number that can be placed in the middle cell,
1
the product of the three numbers in each straight line is .
36 Therefore, the two numbers that are in the same line as 36 are
and . The product of these two numbers is 6.
The two numbers in the same line as 1 are and .
28 NUMINO Challenge D1
