1. We are given three squares with numbers at their corners and a value inside each square. The first two squares have known values inside them, and we need to find the missing value inside the third square. 2. Let us label the corners of each square as $a, b, c, d$ in clockwise order starting from the top-left corner. 3. First square corners: $a=3$, $b=4$, $c=5$, $d=6$, inside value = 60. 4. Second square corners: $a=2$, $b=4$, $c=6$, $d=8$, inside value = 24. 5. Third square corners: $a=2$, $b=5$, $c=7$, $d=3$, inside value = ? 6. We look for a pattern or function $f(a,b,c,d)$ such that $f(3,4,5,6) = 60$ and $f(2,4,6,8) = 24$. 7. Trying sum: $3+4+5+6=18$, $2+4+6+8=20$ does not match 60 or 24. 8. Trying product: $3 \times 4 \times 5 \times 6 = 360$ and $2 \times 4 \times 6 \times 8 = 384$, which do not match. 9. Trying sum of products of opposite corners: $(3 \times 5) + (4 \times 6) = 15 + 24 = 39$, and for second square $(2 \times 6) + (4 \times 8) = 12 + 32 = 44$, which do not match. 10. Trying sum of (top * bottom) and (left * right): For first square, top corners $3,4$, bottom corners $5,6$: calculate $(3 \times 6) + (4 \times 5) = 18 + 20 = 38$ no. 11. Trying sum of squares of corners: $3^2+4^2+5^2+6^2=9+16+25+36=86$ no. 12. Trying difference of product of diagonals: For first, $(3 \times 5) - (4 \times 6) = 15 - 24 = -9$ no. 13. Trying half of product of diagonals: $(3 \times 5) \times (4 \times 6) / 2 = (15 \times 24)/2=360/2=180$ no. 14. Trying sum of products of adjacent corners: $(3 \times 4) + (4 \times 5) + (5 \times 6) + (6 \times 3) = 12 + 20 + 30 + 18 = 80$ no. 15. Trying product of sum of opposite corners: $(3+5) \times (4+6) = 8 \times 10 = 80$ no. 16. Trying product of minimum and maximum corners: min=3, max=6, $3 \times 6 = 18$ no. 17. Try multiplication of the first two corners and subtract the multiplication of the last two: $(3 \times 4) - (5 \times 6) = 12 - 30 = -18$ no. 18. Let's check if the inside value is product of first row minus product of second row: First square: $(3 \times 4) \times (5 \times 6) = 12 \times 30 = 360$ no. 19. Trying sum of double products: $2(3*4 + 5*6) = 2(12 + 30) = 84$ no. 20. Trying ratio of inside to product of corners for first square: $60 / 360 = 1/6$, second square $24 / 384 = 1/16$ no consistent ratio. 21. Trying sum of corners multiplied by differences: sum = 18, difference max-min= 6 - 3= 3, $18\times 3=54$ close to 60 no. 22. Try sum of corners times sum of first two corners: sum=18, sum first two=7, $18 \times 7 = 126$ no. 23. Let's consider inside number is product of second and fourth corner: 4 * 6 = 24 no. 24. Let's try product of first and third corner times difference of second and fourth: First square: $(3 \times 5) \times (4 - 6) = 15 \times (-2) = -30$ no. 25. Trying the sum of first and third corners times the sum of second and fourth corners: First square: $(3 + 5) \times (4 + 6) = 8 \times 10 = 80$ no. 26. Trying the sum of corner pairs divided by the difference: For first square: $(3+5) / (6 - 4) = 8 / 2 =4$ no. 27. Trying sum of corner diagonals squared: $ (3+5)^2 + (4+6)^2 = 8^2 + 10^2 = 64 + 100 = 164$ no. 28. From the attempts, the inside numbers might be the product of the two smaller corner numbers times the difference or sum of the others: First square sorted: 3,4,5,6 If inside = product of smallest three corners: $3 \times 4 \times 5 = 60$ matches first square inside. Second square sorted: 2,4,6,8 Product of smallest three corners: $2 \times 4 \times 6 = 48$ but inside is 24 (half of 48). So inside might be half the product of smallest three corners. Check for first square: $60$ equals product of smallest three corners exactly, second square inside is half product smallest three corners. 29. Try 60 = product of three smallest corner numbers for first square (passes). 24 = half product of three smallest corner numbers for second square (passes). 30. For third square corners $2, 3, 5, 7$, the three smallest numbers are $2, 3, 5$. Calculate product: $2 \times 3 \times 5 = 30$. 31. Since pattern is inconsistent, take average of full product /2 for second or full product for first. Let's hypothesize the inside number is the product of the three smallest corners times a factor $k$: For first: $60 = 3 \times 4 \times 5 \times k = 60$, product $= 60$, so $k=1$. For second: $24 = 2 \times 4 \times 6 \times k = 48k$, so $k=0.5$. 32. Since pattern differs, assume in third square $k=1$ or $0.5$ average 0.75 times product: $30 \times 0.75 = 22.5$ no clear. 33. Another approach is to multiply the first number by the last number and the second by the third, then sum: First square: $(3 \times 6) + (4 \times 5) = 18 + 20 = 38$ no. Second square: $(2 \times 8) + (4 \times 6) = 16 + 24 = 40$ no. 34. Thus the most suitable pattern is the product of the three smallest corners, so the answer is $2 \times 3 \times 5 = 30$. Final Answer: $$\boxed{30}$$