Question

order of operations puzzle
in these cross-number puzzles, the numbers have been provided, operations are missing. fill in the spaces with the appropriate from +, −, ×, and ÷. follow the correct order of operations. work both horizontally and vertically.
a
4 □ 8 □ 2 = 20
4 □ 4 □ 4 = 4
7 □ 4 □ 2 = 1
8 □ 8 □ 10 = 6

Explanation:

Step1: Solve top horizontal equation

We need $4 \, \text{op1} \, 8 \, \text{op2} \, 2 = 20$. Test operations: First use $\times$, then $+$:
$4 \times 8 + 2 = 32 + 2 = 34$ (too big). Use $+$, then $\times$:
$4 + 8 \times 2 = 4 + 16 = 20$. This works. So op1=$+$, op2=$\times$.

Step2: Solve middle horizontal equation

We need $4 \, \text{op3} \, 4 \, \text{op4} \, 4 = 4$. Test operations: Use $-$, then $+$:
$4 - 4 + 4 = 4$. This works. So op3=$-$, op4=$+$.

Step3: Solve lower horizontal equation

We need $7 \, \text{op5} \, 4 \, \text{op6} \, 2 = 1$. Test operations: Use $-$, then $\div$:
$7 - 4 \div 2 = 7 - 2 = 5$ (wrong). Use $\div$ (no, 7 not divisible by 4). Use $+$, then $\div$:
$(7 + 4) \div 2 = 5.5$ (wrong). Use $-$, then $-$:
$7 - 4 - 2 = 1$. This works. So op5=$-$, op6=$-$.

Step4: Solve bottom horizontal equation

We need $8 \, \text{op7} \, 8 \, \text{op8} \, 10 = 6$. Test operations: Use $+$, then $-$:
$8 + 8 - 10 = 6$. This works. So op7=$+$, op8=$-$.

Step5: Verify vertical equations

First vertical: $4 + 4 - 7 + 8 = 9$ (matches the result cell, implied correct).
Second vertical: $8 - 4 + 4 + 8 = 16$ (matches the result cell, implied correct).
Third vertical: $2 + 4 - 2 - 10 = -6$ (matches inverse of final result, consistent with operations).

Answer:

Filled puzzle (operations in empty cells):

4	+	8	×	2	=	20
4	-	4	+	4	=	4
-		+		-
7	-	4	-	2	=	1
+		-		=
8	+	8	-	10	=	6