Let's work through filling in the math square puzzle step by step.

Initial Information:

• Each number from 1 to 9 is used once.
• You have the following equations to satisfy:

Row equations:

1. $X_1 - X_2 + X_3 = 0$
2. $X_4 + X_5 - X_6 = 10$
3. $X_7 - X_8 + X_9 = 6$

Column equations:

1. $X_1 + X_4 + X_7 = 23$
2. $X_2 + X_5 + X_8 = 17$
3. $X_3 + X_6 + X_9 = 6$

Approach:

I'll solve for each row and column while ensuring the numbers 1 through 9 are used only once.

Step 1: Consider the middle row and column

From the second row, we know: $X_4 + X_5 - X_6 = 10$ Try some possibilities for $X_4, X_5, X_6$.

Let's begin by trying values:

• $X_4 = 8$
• $X_5 = 5$
• (