1. **Stating the problem:** We have a grid of equations with numbers 2, 3, 9, and empty circles connected by plus and equals signs. The goal is to find the missing numbers in the empty circles so that all equations hold true. 2. **Understanding the layout:** The first row shows $2 + 3 = 9$, which is not true under normal addition, so this suggests a different operation or pattern. 3. **Analyzing the first equation:** Since $2 + 3 \neq 9$ normally, consider if the plus sign means concatenation or multiplication. For example, $2 \times 3 = 6$, not 9, so multiplication is unlikely. Concatenation $23$ is 23, not 9. 4. **Checking if the sum of digits or squares is used:** $2^2 + 3^2 = 4 + 9 = 13$, not 9. 5. **Hypothesis:** The sum of the numbers in the first row equals 9, so maybe the plus signs represent addition but the numbers in the circles are not the actual values but placeholders or digits of a number. 6. **Looking at the second row:** $2 + \square = 3 + 3 = \square$ suggests the sum of $2 + x$ equals $3 + 3 = 6$, so $2 + x = 6$ which gives $x = 4$. 7. **Filling the missing number:** The empty circle in the second row is 4. 8. **Verifying the third row:** $\square + 3 + \square = $ the sum of the previous row's result. If the previous sum is 6, then $a + 3 + b = 6$. If $a$ and $b$ are the empty circles, and assuming symmetry, $a = b = 1.5$ which is unlikely for integers. 9. **Alternative approach:** Since the puzzle is ambiguous and no explicit operation is given, the best we can do is solve the second row equation: $$2 + x = 3 + 3 = 6 \implies x = 4$$ 10. **Final answer:** The missing number in the second row is 4. This is the only solvable part given the information.