1. **State the problem:** There are four sets of numbers arranged in concentric ovals or around rectangles. - Top-left set: 12, 4, 48, 3, 16 - Top-right set: 15, 14, 210, 21, 10 - Bottom-left set: 7, 6, \boxed{?}, 14, 3 - Bottom-right set: 27, \boxed{?}, 729, 81, 9 We need to find the missing numbers (represented as rectangles) in the bottom-left and bottom-right sets. 2. **Find patterns in top-left set:** Numbers are 12, 4, 48, 3, 16. Check if the middle number (48) relates to others: - Compute $12 \times 4 = 48$, matches the middle number. - Check $3 \times 16 = 48$, also matches. So the middle number is the product of the pairs on each side. 3. **Find patterns in top-right set:** Numbers are 15, 14, 210, 21, 10. Check products: - $15 \times 14 = 210$ matches middle number. - $21 \times 10 = 210$ also matches. Again, the middle number is the product of pairs on the outside. 4. **Apply pattern to bottom-left set:** Numbers are 7, 6, \boxed{?}, 14, 3. Using the pattern, the middle number should be the product of pairs: - Compute $7 \times 6 = 42$ - Compute $14 \times 3 = 42$ Since both equal 42, the missing number is $\boxed{42}$. 5. **Apply pattern to bottom-right set:** Numbers are 27, \boxed{?}, 729, 81, 9. Check pairs that may produce 729: - $27 \times ? = 729$ - $81 \times 9 = 729$ Since $81 \times 9 = 729$, also check $27 \times x = 729$ Divide $729$ by $27$: $$\frac{729}{27} = 27$$ So missing number is $\boxed{27}$. **Final answers:** - Bottom-left missing number: $42$ - Bottom-right missing number: $27$