Write the missing numbers in the blank boxes provided.

First, let's determine the pattern from the examples:

• Example a: Top number is 9. Bottom numbers are 27, 30, 3.
  • $27 \div 3 = 9$ (Top number)
  • $27 + 3 = 30$ (Bottom middle number)
• Example b: Top number is 7. Bottom numbers are 14, 16, 2.
  • $14 \div 2 = 7$ (Top number)
  • $14 + 2 = 16$ (Bottom middle number)

The pattern is:

1. The number in the top circle is the result of dividing the bottom-left number by the bottom-right number.
2. The number in the bottom-middle square is the result of adding the bottom-left number and the bottom-right number.

Now, let's solve each question:

Question 1:

• Bottom left: 24
• Bottom right: 6
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 24 \div 6 = 4$$

• Check: $24 + 6 = 30$ (matches bottom middle). The missing number is $\boxed{\text{4}}$.

Question 2:

• Bottom left: 72
• Bottom right: 6
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 72 \div 6 = 12$$

• Check: $72 + 6 = 78$ (matches bottom middle). The missing number is $\boxed{\text{12}}$.

Question 3:

• Bottom left: 24
• Bottom right: 3
• Missing: Bottom middle square
• Using the pattern: Bottom middle = Bottom left + Bottom right

$$\text{Bottom middle} = 24 + 3 = 27$$

• Check: $24 \div 3 = 8$ (matches top number). The missing number is $\boxed{\text{27}}$.

Question 4:

• Top number: 4
• Bottom middle: 15
• Bottom right: 3
• Missing: Bottom left octagon
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$4 = \text{Bottom left} \div 3$$ $$\text{Bottom left} = 4 \times 3 = 12$$

• Check with the second rule: Bottom middle = Bottom left + Bottom right

$$15 = 12 + 3$$ $$15 = 15$$

The missing number is $\boxed{\text{12}}$.

Question 5:

• Bottom left: 36
• Bottom right: 9
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 36 \div 9 = 4$$

• Check: $36 + 9 = 45$ (matches bottom middle). The missing number is $\boxed{\text{4}}$.

Question 6:

• Top number: 6
• Bottom left: 42
• Bottom middle: 49
• Missing: Bottom right octagon
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$6 = 42 \div \text{Bottom right}$$ $$\text{Bottom right} = 42 \div 6 = 7$$

• Check with the second rule: Bottom middle = Bottom left + Bottom right

$$49 = 42 + 7$$ $$49 = 49$$

The missing number is $\boxed{\text{7}}$.

Question 7:

• Top number: 9
• Bottom middle: 30
• Bottom right: 3
• Missing: Bottom left octagon
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$9 = \text{Bottom left} \div 3$$ $$\text{Bottom left} = 9 \times 3 = 27$$

• Check with the second rule: Bottom middle = Bottom left + Bottom right

$$30 = 27 + 3$$ $$30 = 30$$

The missing number is $\boxed{\text{27}}$.

Question 8:

• Bottom left: 56
• Bottom right: 8
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 56 \div 8 = 7$$

• Check: $56 + 8 = 64$ (matches bottom middle). The missing number is $\boxed{\text{7}}$.

Question 9:

• Bottom left: 16
• Bottom right: 4
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 16 \div 4 = 4$$

• Check: $16 + 4 = 20$ (matches bottom middle). The missing number is $\boxed{\text{4}}$.

Question 10:

• Top number: 5
• Bottom middle: 48
• Bottom right: 8
• Missing: Bottom left octagon
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$5 = \text{Bottom left} \div 8$$ $$\text{Bottom left} = 5 \times 8 = 40$$

• Check with the second rule: Bottom middle = Bottom left + Bottom right

$$48 = 40 + 8$$ $$48 = 48$$

The missing number is $\boxed{\text{40}}$.

Question 11:

• Bottom left: 18
• Bottom right: 2
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 18 \div 2 = 9$$

• Check: $18 + 2 = 20$ (matches bottom middle). The missing number is $\boxed{\text{9}}$.

Question 12:

• Bottom left: 48
• Bottom right: 6
• Missing: Top circle
• Using the pattern: Top number = Bottom left $\div$ Bottom right

$$\text{Top number} = 48 \div 6 = 8$$

• Check: $48 + 6 = 54$ (matches bottom middle). The missing number is $\boxed{\text{8}}$.