1. **Stating the problem:** We need to find the number replacing the question mark (?) inside the third triangle given the pattern from the first two triangles. 2. **Observing the given triangles:** - Triangle 1 vertices: 6 (top), 2 (bottom-left), 3 (bottom-right), inside number: 30 - Triangle 2 vertices: 5 (top), 4 (bottom-left), 1 (bottom-right), inside number: 25 - Triangle 3 vertices: 4 (top), 6 (bottom-left), 2 (bottom-right), inside number: ? 3. **Finding the pattern:** Check if the inside number relates to the vertices by multiplication or addition. 4. **Testing multiplication:** - Triangle 1: $6 \times 2 \times 3 = 36$, but inside number is 30, so not direct multiplication. - Triangle 2: $5 \times 4 \times 1 = 20$, inside number is 25, so no direct multiplication. 5. **Testing sum of vertices:** - Triangle 1: $6 + 2 + 3 = 11$, inside number 30, no direct relation. 6. **Testing sum of squares:** - Triangle 1: $6^2 + 2^2 + 3^2 = 36 + 4 + 9 = 49$, inside number 30, no match. 7. **Testing sum of products of pairs:** - Triangle 1: $(6 \times 2) + (2 \times 3) + (3 \times 6) = 12 + 6 + 18 = 36$, inside number 30, close but no. 8. **Testing sum of vertices multiplied by the top vertex:** - Triangle 1: $6 \times (2 + 3) = 6 \times 5 = 30$, matches inside number. - Triangle 2: $5 \times (4 + 1) = 5 \times 5 = 25$, matches inside number. 9. **Applying the pattern to Triangle 3:** - Top vertex: 4 - Bottom-left + bottom-right: $6 + 2 = 8$ - Inside number: $4 \times 8 = 32$ 10. **Answer:** The number replacing (?) is 32. **Final answer: 32**