Page 146 - NUMINO Challenge_D1
P. 146
3 Numbers from 1 to 8 are consecutive numbers, Type 3-2 Multiplication Magic Square p.28~p.29
and the sum of the greatest and smallest
numbers is 9. (1, 8), (2, 7), (3, 6), (4, 5) 1 The given numbers are divisors of 36. Therefore,
2 pair the numbers such that the product of each
1 pair of numbers is 36. Put the remaining number
35 46 in the middle square.
8
7 1 2 3 4 6 9 12 18 36
Answers will vary.
Problem solving
1 First, put 11 in the middle , so that the sum of 2 6, 216, 2, 3, 12, 18
the three numbers is the greatest possible sum. 12 1 18
Then, pair the remaining numbers, such that the 964
sum of each pair is 11. 2 36 3
11 Problem solving
11
11 1 The numbers on each vertex are multiplied
1 2 3 4 5 6 7 8 9 10 11
twice, so use the three smallest numbers or the
11 three greatest numbers. Write the numbers such
11 that the products of numbers in each straight
line are equal.
12
10 9
5 6 11 8 3
7
4
Answers will vary. 18 2
2 Since the sum of numbers from 1 to 16 is 136, 21 6 18
the sum of the four numbers in each straight line 6 3 12 or 3 12 1
is 136 4 34. In each straight line, the sum of Answers will vary.
the two inner numbers and the two outer
numbers must be equal, so that the sums of the 2 is a divisor of 6 and 15, therefore it can be 1
eight numbers on each octagon are equal. The
pairs of numbers that add up to 17 are (1, 16), or 3. But, when 1, must be 15, which is
(2, 15), (3, 14), (4, 13), (5, 12), (6, 11), (7, 10), and not possible. Therefore, 3, 2 and
(8, 9). Write the numbers in the , such that the 5. The product of and is 14, so 7, and
two numbers on the inside and the outside form the product of and is 45, therefore 9.
the pairs given above.
15 7
63 14
4 1 10 63 14 92
14 8
45 6 45 6
6 12 5 11 15
5 15 3
9 16 3
13
7
2
Answers will vary.
Answer Key
and the sum of the greatest and smallest
numbers is 9. (1, 8), (2, 7), (3, 6), (4, 5) 1 The given numbers are divisors of 36. Therefore,
2 pair the numbers such that the product of each
1 pair of numbers is 36. Put the remaining number
35 46 in the middle square.
8
7 1 2 3 4 6 9 12 18 36
Answers will vary.
Problem solving
1 First, put 11 in the middle , so that the sum of 2 6, 216, 2, 3, 12, 18
the three numbers is the greatest possible sum. 12 1 18
Then, pair the remaining numbers, such that the 964
sum of each pair is 11. 2 36 3
11 Problem solving
11
11 1 The numbers on each vertex are multiplied
1 2 3 4 5 6 7 8 9 10 11
twice, so use the three smallest numbers or the
11 three greatest numbers. Write the numbers such
11 that the products of numbers in each straight
line are equal.
12
10 9
5 6 11 8 3
7
4
Answers will vary. 18 2
2 Since the sum of numbers from 1 to 16 is 136, 21 6 18
the sum of the four numbers in each straight line 6 3 12 or 3 12 1
is 136 4 34. In each straight line, the sum of Answers will vary.
the two inner numbers and the two outer
numbers must be equal, so that the sums of the 2 is a divisor of 6 and 15, therefore it can be 1
eight numbers on each octagon are equal. The
pairs of numbers that add up to 17 are (1, 16), or 3. But, when 1, must be 15, which is
(2, 15), (3, 14), (4, 13), (5, 12), (6, 11), (7, 10), and not possible. Therefore, 3, 2 and
(8, 9). Write the numbers in the , such that the 5. The product of and is 14, so 7, and
two numbers on the inside and the outside form the product of and is 45, therefore 9.
the pairs given above.
15 7
63 14
4 1 10 63 14 92
14 8
45 6 45 6
6 12 5 11 15
5 15 3
9 16 3
13
7
2
Answers will vary.
Answer Key