Question

5 □ 4 □ 2 = 18
4 □ 2 □ 1 = 9
5 □ 3 □ 2 = 4
25 □ = □
□ 5 □ 1 = 6

Explanation:

Step1: Solve top row (sum=18)

Let blanks be $a, b$. Equation: $5 + a + 4 + b + 2 = 18$
$\implies 11 + a + b = 18 \implies a + b = 7$

Step2: Solve leftmost column (sum=25)

Let blank be $c$. Equation: $5 + c + 4 + 5 = 25$
$\implies 14 + c = 25 \implies c = 11$

Step3: Solve 3rd row (sum=9)

Let blanks be $d, e$. Equation: $4 + d + 2 + e + 1 = 9$
$\implies 7 + d + e = 9 \implies d + e = 2$

Step4: Solve 5th row (sum=4)

Let blank be $f$. Equation: $5 + f + 3 + 2 = 4$
$\implies 10 + f = 4 \implies f = -6$

Step5: Solve 7th row (sum=6)

Let blank be $g$. Equation: $25 + g + 5 + 1 = 6$
$\implies 31 + g = 6 \implies g = -25$

Step6: Solve 3rd column (sum unknown)

Let sum be $S_3$. Equation: $4 + 2 + 3 + 5 = S_3$
$\implies S_3 = 14$

Step7: Solve 5th column (sum unknown)

Let sum be $S_5$. Equation: $2 + 1 + 2 + 1 = S_5$
$\implies S_5 = 6$

Step8: Solve 2nd column (sum unknown)

Let sum be $S_2$. Equation: $a + c + d + f + g = S_2$
$\implies a + 11 + d -6 -25 = S_2 \implies a + d -20 = S_2$

Step9: Solve 4th column (sum unknown)

Let sum be $S_4$. Equation: $b + e + 2 + 1 = S_4$
$\implies b + e + 3 = S_4$

Answer:

Filled grid (with derived values, assuming standard row/column sums):

5	$a$	4	$b$	2	=	18
4	$d$	2	$e$	1	=	9
█	█	█	█	█	█
5	$f$	3	2		=	4
=	█	=	█	=	█	=
25	$g$	5	1		=	6

With calculated fixed values:
$c=11$, $f=-6$, $g=-25$, $a+b=7$, $d+e=2$
Column sums: 3rd column = 14, 5th column = 6