1. **Restate the Problem:** We have four triangles, each divided into four sections around a center circle with numbers inside or empty. The top-left, top-right, and bottom-right triangles have numbers inside the center circle: 36, 80, and 210 respectively. The bottom-left triangle's center circle is blank. Each triangle has four numbers around the circle, arranged clockwise: - Top-left: 3, 2, 1, 6 (circle 36) - Top-right: 4, 4, 5, 1 (circle 80) - Bottom-left: 6, 8, 2, 4 (circle blank) - Bottom-right: 5, 7, square, 2 (circle 210) The goal is to find the missing number represented by the square in the bottom-right triangle and likely the number inside the blank circle in the bottom-left. 2. **Analyze Given Patterns:** Check relationships between the numbers around the circle and the number inside the circle for the triangles with known center values. - Top-left triangle: Numbers: 3, 2, 1, 6 Center: 36 Try multiplication or sum of products: $3 \times 2 \times 1 \times 6 = 36$ This exactly matches the center number. - Top-right triangle: Numbers: 4, 4, 5, 1 Center: 80 Check product: $4 \times 4 \times 5 \times 1 = 80$ Matches the center number again. - Bottom-right triangle: Numbers: 5, 7, square, 2 Center: 210 Try same pattern: $5 \times 7 \times \text{square} \times 2 = 210$ Calculate known product: $5 \times 7 \times 2 = 70$ So $$70 \times \text{square} = 210$$ Divide both sides by 70: $$\text{square} = \frac{210}{70} = 3$$ 3. **Find missing number in bottom-left triangle:** Numbers: 6, 8, 2, 4 Center: blank Since pattern is product of 4 numbers, Compute: $$6 \times 8 \times 2 \times 4 = 384$$ So the center number is 384. 4. **Final answers:** - Number in square = 3 - Number inside blank circle = 384 These are consistent with the pattern discovered. **Final step:** The square symbol represents the number 3, and the bottom-left center circle number is 384.