1. Problem: Determine the missing number in the third square's top-right corner based on the pattern in the given squares. 2. Given squares: - First square vertices: 8 (top-left), 4 (top-right), 3 (bottom-right), 6 (bottom-left) - Second square vertices: 15 (top-left), 5 (top-right), 9 (bottom-right), 12 (bottom-left) - Third square vertices: 21 (top-left), ? (top-right), 2 (bottom-right), 7 (bottom-left) 3. Observing the pattern in the first two squares: - For the first square: Sum of opposite corners: $$8 + 3 = 11$$ $$4 + 6 = 10$$ - For the second square: $$15 + 9 = 24$$ $$5 + 12 = 17$$ 4. Another approach is to check if the sum of all vertices equals a certain number or if there is a relation between the numbers. - First square sum: $$8 + 4 + 3 + 6 = 21$$ - Second square sum: $$15 + 5 + 9 + 12 = 41$$ 5. Check if the top-left vertex relates to the sum of the other three vertices: - First square: $$8 = 4 + 3 + 6 - 5$$ (No clear relation) - Second square: $$15 = 5 + 9 + 12 - 11$$ (No clear relation) 6. Check the difference between top-left and bottom-left vertices: - First square: $$8 - 6 = 2$$ - Second square: $$15 - 12 = 3$$ - Third square: $$21 - 7 = 14$$ 7. Check the difference between top-right and bottom-right vertices: - First square: $$4 - 3 = 1$$ - Second square: $$5 - 9 = -4$$ - Third square: $$? - 2 = ?$$ 8. Since no clear arithmetic pattern emerges, consider the possibility that the missing number is the quotient of the top-left vertex divided by the bottom-left vertex: - First square: $$8 \div 6 \approx 1.33$$ - Second square: $$15 \div 12 = 1.25$$ - Third square: $$21 \div 7 = 3$$ 9. The top-right vertex might be the difference between the top-left and bottom-left vertices: - First square: $$8 - 6 = 2$$ (Given 4, so no) - Second square: $$15 - 12 = 3$$ (Given 5, no) 10. Alternatively, check if the missing number is the quotient of bottom-left vertex divided by bottom-right vertex: - First square: $$6 \div 3 = 2$$ (Given 4, no) - Second square: $$12 \div 9 = 1.33$$ (Given 5, no) 11. Since the problem states "প্রতিটি বর্গে মোটিকোণে কতটি সংখ্যা থাকার কথা। শূন্য খানে কোনটি হবে?" (What number should be in the blank square?), and the options are ১২, ১৬, ১৮, ১৯. 12. Considering the pattern of the top-left vertex being the sum of the other three vertices minus a constant: - First square: $$8 = 4 + 3 + 6 - 5$$ - Second square: $$15 = 5 + 9 + 12 - 11$$ - Third square: $$21 = ? + 2 + 7 - x$$ 13. Calculate the sum of known vertices in the third square: $$2 + 7 = 9$$ 14. Let the missing number be $x$. Then: $$21 = x + 9 - c$$ 15. Assuming the constant $c$ is increasing by 6 (from 5 to 11), next $c$ is 17: $$21 = x + 9 - 17$$ $$x = 21 + 17 - 9 = 29$$ (Not in options) 16. Alternatively, check if the missing number is the average of the other three vertices: $$\frac{21 + 2 + 7}{3} = \frac{30}{3} = 10$$ (Not in options) 17. Since the options are ১২, ১৬, ১৮, ১৯, and the closest logical number is ১৬ (16), select ১৬. Final answer: ১৬