Oval Missing Values
1. The problem involves identifying the missing numbers (☐) in two sets of concentric ovals based on given numerical patterns.
2. Let's analyze the patterns in the known ovals to find the relationship:
Top-left oval numbers (clockwise): 12, 4, 48, 3, 16
- Notice that $12 \times 4 = 48$ and $3 \times 16 = 48$.
- Thus, the product of opposite numbers equals 48.
Top-right oval numbers (clockwise): 15, 14, 210, 21, 10
- Check products of opposites:
- $15 \times 14 = 210$
- $21 \times 10 = 210$
- So, the opposite pairs multiply to 210.
3. Apply this reasoning to bottom-left oval (clockwise): 7, 6, ☐, 14, 3
- We assume the product of opposite numbers is constant.
- Opposite pairs are (7, 6), (☐, 14), and (3) at center or side. With 5 numbers, and given pattern, the product is likely consistent.
- $7 \times 6 = 42$
- $14 \times ? = 42$ so missing number $= \frac{42}{14} = 3$
- The missing number is $3$.
4. Bottom-right oval (clockwise): 27, ☐, 729, 81, 9
- Using the same logic, find the product of opposites:
- $27 \times ? = ?$
- Check $81 \times 9 = 729$
- So, likely product of opposites is 729
- Missing number $= \frac{729}{27} = 27$
Final answers:
- Bottom-left missing number: $3$
- Bottom-right missing number: $27$