Math puzzle worksheet with integers for educational practice.

To solve this puzzle, we need to fill in the empty white boxes so that the numbers in each connected block (either a row or a column) add up to zero. This is like a balance scale; the positive and negative numbers must cancel each other out.

Let's break it down block by block.

1. Top Left Horizontal Block
* Numbers: $13$, $-1$, [Empty], $+6$
* Goal: Sum = $0$
* Calculation:
* Add the known numbers: $13 + (-1) + 6 = 12 + 6 = 18$.
* To get to $0$, we need the opposite of $18$.
* $18 + (-18) = 0$.
* Result: The empty box is $-18$.

2. Middle Left Horizontal Block
* Numbers: [Empty], $-7$, [Empty], $-8$
* Clue: The first empty box is part of a vertical column on the far left. Let's solve that column first to find this number.

3. Far Left Vertical Column
* Numbers: [Top Empty], [Middle Empty], $+17$, [Bottom Empty], $-1$
* Wait, looking at the grid structure:
* The top box of this column is the one we just found: $-18$.
* The next box down is the start of the middle horizontal row. Let's call this $A$.
* The next box is $+17$.
* The next box is empty. Let's call this $B$.
* The bottom box is $-1$.
* So the column is: $-18, A, 17, B, -1$.
* We have two unknowns here ($A$ and $B$). Let's look for another connection.

Let's restart with blocks that have only one missing number.

Step 1: Top Left Horizontal Row
* Cells: $13, -1, \text{[Box 1]}, +6$
* Sum: $13 - 1 + 6 = 18$.
* Missing number: $0 - 18 = \mathbf{-18}$.
* Box 1 is $-18$.

Step 2: Top Right Vertical Column (Part 1)
* Looking at the top right area, there is a vertical segment.
* Cells: $\text{[Box 2]}, -2, \text{[Box 3]}, +5, \text{[Box 4]}, -4, \text{[Box 5]}$
* This looks like one long column. Let's trace it carefully.
* Top cell: Box 2.
* Next: $-2$.
* Next: Box 3.
* Next: $+5$.
* Next: Box 4.
* Next: $-4$.
* Bottom: Box 5.
* This column has too many unknowns. Let's look for intersections.

Let's identify all distinct "words" (connected lines of cells).

Horizontal Words:
1. H1 (Top Left): $13, -1, \text{[H1-3]}, +6$.
* Sum known: $18$. Missing: $\mathbf{-18}$.
2. H2 (Middle Left): $\text{[H2-1]}, -7, \text{[H2-3]}, -8$.
* H2-1 is also part of Vertical Column V1.
* H2-3 is also part of Vertical Column V2? No, let's look at the grid again.
* Actually, let's look at the vertical columns first, as some are clearer.

Vertical Columns:
1. V1 (Far Left): Starts below H1.
* The cell above $+17$ is H2-1.
* The cell below $+17$ is $\text{[V1-3]}$.
* The cell below that is $-1$.
* Wait, does V1 include the top cell from H1? No, H1 is a separate horizontal block. The vertical block usually starts where the horizontal one ends or intersects.
* Let's assume standard crossword rules: A "word" is a continuous line of shaded/numbered cells separated by black space or grid edges.
* V1 (Leftmost column): It seems to consist of 4 cells: The one shared with H2 (let's call it $X$), then $+17$, then an empty one ($Y$), then $-1$.
* Equation: $X + 17 + Y + (-1) = 0 \Rightarrow X + Y + 16 = 0 \Rightarrow X + Y = -16$.
* We need $X$ or $Y$ from elsewhere.

2. H2 (Middle Left Row):
* Cells: $X, -7, Z, -8$.
* Equation: $X - 7 + Z - 8 = 0 \Rightarrow X + Z - 15 = 0 \Rightarrow X + Z = 15$.

3. V2 (Middle Column):
* Top cell is shared with H1? No, H1 ends at $+6$. The cell below $+6$ is empty. Let's look at the structure.
* There is a vertical column starting with $-2$.
* Let's trace the column containing $-2, +5, -4$.
* Above $-2$ is an empty cell (let's call it $A$).
* Below $-2$ is an empty cell (let's call it $B$).
* Below $B$ is $+5$.
* Below $+5$ is an empty cell (let's call it $C$).
* Below $C$ is $-4$.
* Below $-4$ is an empty cell (let's call it $D$).
* This seems complicated. Let's look for simpler connections.

Let's re-examine the grid layout based on typical puzzles of this type.
Usually, gray boxes are "clues" or fixed numbers, and white boxes are to be filled. But here, some white boxes have numbers ($13, -1, +6$, etc.) and some are empty. The prompt implies filling the *empty* white boxes.

Let's label every empty white box with a variable.

Row 1 (Top Left):
$[13] [-1] [\text{E1}] [+6]$
Sum: $13 - 1 + 6 = 18$.
$\text{E1} + 18 = 0 \rightarrow \mathbf{E1 = -18}$.

Column 1 (Far Left, below Row 1):
The box $\text{E1}$ is at the end of Row 1. Is it part of a vertical column?
Looking at the grid lines:
- Row 1 has 4 cells.
- Below the 3rd cell ($\text{E1}$) is... nothing? Or is it connected to the block below?
- Let's look at the block starting with $+17$.
- To the left of $+17$ is a column.
- Let's trace the column on the far left edge.
- Top cell: Part of Row 2?
- Let's define Row 2 (the one with $-7$).
- Row 2 cells: $[\text{E2}], [-7], [\text{E3}], [-8]$.
- $\text{E2}$ is directly below the $-1$ from Row 1? No, visually $\text{E2}$ is below the $13$? No, the grid is staggered.

Let's look at vertical alignments strictly.
- Col 1: Contains $\text{E2}$ (from Row 2), $+17$, $\text{E4}$, $-1$.
- Wait, is $\text{E2}$ the top of this column? Yes, it seems so.
- So Col 1 is: $\text{E2}, +17, \text{E4}, -1$.
- Sum: $\text{E2} + 17 + \text{E4} - 1 = 0 \rightarrow \text{E2} + \text{E4} + 16 = 0 \rightarrow \mathbf{\text{E2} + \text{E4} = -16}$. (Eq 1)

- Row 2: $\text{E2}, -7, \text{E3}, -8$.
- Sum: $\text{E2} - 7 + \text{E3} - 8 = 0 \rightarrow \text{E2} + \text{E3} - 15 = 0 \rightarrow \mathbf{\text{E2} + \text{E3} = 15}$. (Eq 2)

- Col 2: This column contains $\text{E3}$ (from Row 2). What else?
- Above $\text{E3}$ is $\text{E1}$ ($-18$). Are they connected?
- Visually, $\text{E1}$ is in Row 1, Col 3. $\text{E3}$ is in Row 2, Col 3.
- If they are connected vertically, the column would be $\text{E1}, \text{E3}$.
- Let's check if there are other cells. Below $\text{E3}$? The grid shows a gap or the start of another block?
- Looking at the image, below $\text{E3}$ (which is next to $-8$) is empty space.
- However, to the right of $\text{E3}$ is $-8$.
- Let's look at the column containing $-2$.

Let's try a different approach: Identify independent chains.

Chain A: Top Left Horizontal
Cells: $13, -1, \text{E1}, 6$.
Sum: $18 + \text{E1} = 0 \Rightarrow \mathbf{\text{E1} = -18}$.

Chain B: The "L" shape or intersection at E1?
Is $\text{E1}$ part of a vertical column?
Looking at the grid, below $\text{E1}$ is the cell $\text{E3}$?
Let's assume standard grid alignment.
Row 1: Col 1($13$), Col 2($-1$), Col 3($\text{E1}$), Col 4($6$).
Row 2: Col 1($\text{E2}$), Col 2($-7$), Col 3($\text{E3}$), Col 4($-8$).
If this alignment holds:
- Col 3 consists of $\text{E1}$ and $\text{E3}$.
- Sum: $\text{E1} + \text{E3} = 0$.
- Since $\text{E1} = -18$, then $-18 + \text{E3} = 0 \Rightarrow \mathbf{\text{E3} = 18}$.

Now we can solve for $\text{E2}$ using Row 2 equation.
- Row 2: $\text{E2}, -7, \text{E3}, -8$.
- $\text{E2} - 7 + 18 - 8 = 0$.
- $\text{E2} + 3 = 0 \Rightarrow \mathbf{\text{E2} = -3}$.

Now we can solve for $\text{E4}$ using Col 1 equation.
- Col 1 (below Row 1): The cells are $\text{E2}, +17, \text{E4}, -1$.
- Note: Does Col 1 include the cell above $\text{E2}$? That would be $-1$ from Row 1.
- If Col 1 is $-1, \text{E2}, 17, \text{E4}, -1$:
- Sum: $-1 + (-3) + 17 + \text{E4} - 1 = 0$.
- $12 + \text{E4} = 0 \Rightarrow \mathbf{\text{E4} = -12}$.
- Let's verify if the top cell ($-1$) is part of this vertical word.
- In crosswords, usually if a cell is part of a horizontal word, it *can* be part of a vertical word if the vertical word continues through it.
- However, often "blocks" are separated. Let's look at the shading.
- The box with $-1$ (Row 1, Col 2) is gray. The box with $13$ is gray.
- Usually, the gray boxes are the "given" numbers. The white boxes are the ones to fill.
- BUT, in this specific puzzle style ("Math Crossword" or "Cross Sums"), typically all cells in a line sum to zero. The gray/white distinction might just be for visual separation or indicating givens vs blanks.
- Crucial observation: The prompt asks to solve the problem. The empty boxes are the unknowns. The numbered boxes (gray and white) are knowns.
- Let's re-read the visual cues.
- $13, -1, 6$ are in gray/white mixed? No, $13$ is white, $-1$ is gray, empty is white, $6$ is gray.
- Actually, looking closely:
- $13$ (White), $-1$ (Gray), Empty (White), $+6$ (Gray).
- This suggests Gray = Given, White = To Fill OR Given?
- But $13$ is White and given. So White can be given.
- The Empty boxes are definitely the unknowns.

Let's stick to the connectivity logic.

Hypothesis 1: Vertical connectivity exists between rows.

Left Section:
1. Row 1: $13, -1, \text{E1}, 6$. Sum = $18$. $\text{E1} = \mathbf{-18}$.
2. Col 3 (connecting R1 and R2): $\text{E1}$ and $\text{E3}$.
- If they form a vertical pair: $\text{E1} + \text{E3} = 0 \Rightarrow \text{E3} = \mathbf{18}$.
3. Row 2: $\text{E2}, -7, \text{E3}, -8$.
- Sum: $\text{E2} - 7 + 18 - 8 = \text{E2} + 3 = 0 \Rightarrow \text{E2} = \mathbf{-3}$.
4. Col 1 (connecting R1 and R2 and below):
- Cells: $-1$ (from R1), $\text{E2}$, $17$, $\text{E4}$, $-1$ (bottom).
- Let's check if $-1$ (R1, Col 2) connects to $\text{E2}$ (R2, Col 1)? No, different columns.
- Let's check Col 1 specifically.
- Col 1 contains: $\text{E2}$ (R2), $17$ (R3), $\text{E4}$ (R4), $-1$ (R5).
- Does it extend up to R1? R1 Col 1 is $13$.
- If Col 1 is $13, \text{E2}, 17, \text{E4}, -1$:
- Sum: $13 + (-3) + 17 + \text{E4} - 1 = 26 + \text{E4} = 0 \Rightarrow \text{E4} = -26$.
- If Col 1 starts at $\text{E2}$:
- Sum: $-3 + 17 + \text{E4} - 1 = 13 + \text{E4} = 0 \Rightarrow \text{E4} = -13$.

Which is more likely?
Look at the border between $13$ and $\text{E2}$. There is a horizontal line separating Row 1 and Row 2. In many such puzzles, a solid line indicates a break in the word. However, in the "Cross Sums" puzzle type, words continue unless blocked by black. Here, there are no black blocks, just grid lines.

Let's look at the right side to find a pattern.

Right Section:
There is a tall vertical column on the right-ish side.
Cells: $\text{E5}$ (top), $-2$, $\text{E6}$, $+5$, $\text{E7}$, $-4$, $\text{E8}$ (bottom).
And horizontal branches?

Let's trace the connections on the right.

Top Right Horizontal:
Cells: $\text{E9}$ (left), $\text{E5}$ (middle?), $+13$ (right)?
Let's look at the top right cluster.
Row: Empty, $-2$, Empty, $+13$.
Wait, $-2$ is in a vertical column.
Let's assume the grid coordinates:

Let's map the grid more precisely.

Block 1 (Top Left Horiz):
$[13] [-1] [\text{A}] [+6]$
Sum: $13-1+6 = 18$. $\text{A} = \mathbf{-18}$.

Block 2 (Left Vert):
This column aligns with the first cell of the row below?
Let's look at the second row down on the left: $[\text{B}] [-7] [\text{C}] [-8]$.
$\text{B}$ is under $13$? Or under $-1$?
Visually, $\text{B}$ is under $13$. $\text{C}$ is under $\text{A}$ ($-18$).

If $\text{C}$ is under $\text{A}$, do they form a vertical word?
If yes: $\text{A} + \text{C} = 0 \Rightarrow -18 + \text{C} = 0 \Rightarrow \text{C} = \mathbf{18}$.

Now solve Row 2: $[\text{B}] [-7] [\text{C}=18] [-8]$.
Sum: $\text{B} - 7 + 18 - 8 = \text{B} + 3 = 0 \Rightarrow \text{B} = \mathbf{-3}$.

Now, what about the column containing $\text{B}$?
It goes down: $[\text{B}] [+17] [\text{D}] [-1]$.
Does it go up to $13$?
If it includes $13$: $13 + \text{B} + 17 + \text{D} - 1 = 0$.
$13 - 3 + 17 + \text{D} - 1 = 26 + \text{D} = 0 \Rightarrow \text{D} = -26$.
If it does NOT include $13$ (starts at B): $\text{B} + 17 + \text{D} - 1 = 0$.
$-3 + 17 + \text{D} - 1 = 13 + \text{D} = 0 \Rightarrow \text{D} = -13$.

Let's look for clues in the rest of the puzzle to determine if vertical words span across the horizontal dividing lines.

Look at the central vertical column:
Top cell: $\text{E}$ (under $+6$? No, $+6$ is end of row).
Let's look at the column with $-2$.
Above $-2$ is an empty cell $\text{F}$.
To the left of $\text{F}$ is $+6$? No.
To the right of $\text{F}$ is $+13$?

Let's trace the Top Right Horizontal Row.
It seems to be: $[\text{G}] [-2] [\text{H}] [+13]$.
Wait, $-2$ is gray. $\text{G}, \text{H}$ are white/empty.
If this is a row: $\text{G} - 2 + \text{H} + 13 = 0 \Rightarrow \text{G} + \text{H} + 11 = 0$.

Now, look at the vertical column passing through $-2$.
Cells: $\text{F}$ (above $-2$), $-2$, $\text{I}$ (below $-2$), $+5$, $\text{J}$ (below $+5$), $-4$, $\text{K}$ (below $-4$).

This is getting complex. Let's look at the very bottom right.
Column: $[\text{L}] [-1]$.
Row connected to $\text{L}$? $[\text{M}] [+8]$.

Let's try to interpret the "blocks" as contiguous segments separated by grid boundaries that act as walls.
Usually, in these worksheets, a thick line or a shift in alignment indicates a new word.

Let's look at the provided solution structure from similar online puzzles ("Cross Number Puzzles").
Rule: Every straight line of connected cells sums to 0.

Let's re-evaluate the Left Side with the assumption that vertical lines do NOT cross horizontal lines unless explicitly drawn as one continuous strip.
Looking at the image, the grid lines are uniform. However, the blocks are offset.

Left Side Analysis:
1. Top Row: $13, -1, \text{A}, 6$. Sum=18. $\text{A} = \mathbf{-18}$.
2. Vertical Pair? Cell $\text{A}$ is above Cell $\text{C}$. Is there a line between them? Yes, a grid line. But is it a "wall"?
- Look at the column with $+17$. It has 4 cells.
- Look at the column with $-2$. It has 7 cells?

Let's look at the Right Side which might be self-contained.

Central/Right Vertical Column:
Cells: $\text{Top1}$, $-2$, $\text{Mid1}$, $+5$, $\text{Mid2}$, $-4$, $\text{Bot1}$.

Top Right Horizontal Row:
Cells: $\text{Top1}$, $-2$, $\text{Top2}$, $+13$.
Note: $\text{Top1}$ is shared.

Right Edge Vertical Column:
Cells: $\text{Top2}$, $-9$, $\text{Right1}$, $-1$.
Wait, $-9$ is below $+13$?
Let's trace the rightmost edge.
Top cell: $\text{Top2}$ (from the horiz row).
Below it: $-9$.
Below that: $\text{Right1}$.
Below that: $-1$.
Is this a single column?
Sum: $\text{Top2} - 9 + \text{Right1} - 1 = 0 \Rightarrow \text{Top2} + \text{Right1} = 10$.

Also, $\text{Right1}$ is part of a horizontal row?
Row: $\text{Mid2}$ (from center col), $+8$, $\text{Right1}$?
Let's check the bottom right cluster.
Horizontal: $\text{Mid2}$, $+8$, $\text{Right1}$?
Or is $+8$ in a row with $\text{Right1}$?
Visually:
Center Col ends with $\text{Bot1}$.
To the right of $\text{Bot1}$ is $+8$?
To the right of $+8$ is $\text{Right1}$?

Let's refine the Grid Map.

Col 4 (Center-Right):
1. $\text{C4-R1}$: Empty (part of Top Right Horiz)
2. $\text{C4-R2}$: $-2$
3. $\text{C4-R3}$: Empty
4. $\text{C4-R4}$: $+5$
5. $\text{C4-R5}$: Empty
6. $\text{C4-R6}$: $-4$
7. $\text{C4-R7}$: Empty

Col 5 (Far Right):
1. $\text{C5-R1}$: Empty (part of Top Right Horiz, next to $+13$?)
- Wait, the Top Right Horiz is: $\text{C4-R1}$, $-2$ (Wait, $-2$ is C4-R2?).

Let's look at the image again very carefully.

Top Right Block:
Row: [Empty] [Empty] [+13] ??
No. The box with $-2$ is to the left of the box with $+13$?
Actually, looking at the alignment:
The box with $-2$ is in the same column as $+5$ and $-4$.
The box with $+13$ is to the RIGHT of the empty box above $-2$?

Let's assume the following structure for the Top Right:
Horizontal Row: [Empty A] [Empty B] [+13] -> This doesn't fit the $-2$.

Let's try:
Horizontal Row: [Empty A] [-2] [Empty B] [+13]
If this is a row, then $-2$ is in the row.
Then there is a Vertical Column passing through $-2$.
Col: [Empty C] [-2] [Empty D] [+5] [Empty E] [-4] [Empty F]

If $-2$ is in both, then:
Row Sum: $\text{A} - 2 + \text{B} + 13 = 0 \Rightarrow \text{A} + \text{B} = -11$.
Col Sum: $\text{C} - 2 + \text{D} + 5 + \text{E} - 4 + \text{F} = 0 \Rightarrow \text{C} + \text{D} + \text{E} + \text{F} - 1 = 0$.

Now, look at Empty A. It is above Empty C?
If they are connected vertically:
Col Left of -2: [Empty A] [Empty C] ...?

This is too ambiguous without a clear grid. Let's look for a simpler interpretation.

Alternative Interpretation: Independent Blocks
Maybe the lines don't cross?
1. Top Left Horiz: $13, -1, \text{A}, 6$. $\text{A} = -18$.
2. Left Vert: $\text{B}, 17, \text{C}, -1$.
3. Mid Left Horiz: $\text{D}, -7, \text{E}, -8$.
4. Connection: $\text{B}$ is above $\text{D}$? $\text{A}$ is above $\text{E}$?

If $\text{A}$ and $\text{E}$ are connected vertically:
$\text{A} + \text{E} = 0 \Rightarrow -18 + \text{E} = 0 \Rightarrow \text{E} = 18$.

If $\text{E} = 18$:
Mid Left Horiz: $\text{D} - 7 + 18 - 8 = 0 \Rightarrow \text{D} + 3 = 0 \Rightarrow \text{D} = -3$.

If $\text{B}$ and $\text{D}$ are connected vertically:
Are they in the same column?
$\text{D}$ is the first cell of Mid Left Horiz.
$\text{B}$ is the first cell of Left Vert.
Visually, $\text{B}$ is directly above $\text{D}$.
Do they form a column with the cells above/below?
Above $\text{B}$ is $-1$ (from Top Left Horiz).
If Col 1 is: $-1, \text{B}, 17, \text{C}, -1$.
Sum: $-1 + \text{B} + 17 + \text{C} - 1 = 0 \Rightarrow \text{B} + \text{C} + 15 = 0$.

We need another link.
Is $\text{B}$ connected to anything else?
If $\text{B}$ and $\text{D}$ are the same cell? No, they are in different rows.

Let's assume the standard "Crossword" rule: Words intersect.

Intersection 1: Cell $\text{E}$ (from Mid Left Horiz) and Cell $\text{A}$ (from Top Left Horiz).
They are in the same vertical column (Col 3).
Word: $\text{A}, \text{E}$.
Sum: $\text{A} + \text{E} = 0$.
$\text{A} = -18 \Rightarrow \mathbf{\text{E} = 18}$.

Intersection 2: Cell $\text{D}$ (from Mid Left Horiz) and Cell $\text{B}$ (from Left Vert).
They are in the same vertical column (Col 1).
But wait, $\text{D}$ is Row 2, $\text{B}$ is Row 2? No.
$\text{D}$ is the first cell of the row starting with $-7$.
$\text{B}$ is the first cell of the column starting with $17$?
Visually, $\text{B}$ IS $\text{D}$. They are the same box.
Let's call this box $\text{X}$.

So, Box X is part of:
1. Horizontal Row: $\text{X}, -7, \text{E}(18), -8$.
2. Vertical Column: $\text{X}, 17, \text{Y}, -1$. (Does it include the cell above X?)

Let's solve for $\text{X}$ using the Horizontal Row:
$\text{X} - 7 + 18 - 8 = 0$
$\text{X} + 3 = 0$
$\mathbf{\text{X} = -3}$.

Now use $\text{X} = -3$ in the Vertical Column.
Column cells: $\text{X}(-3), 17, \text{Y}, -1$.
Does it include the cell above $\text{X}$?
The cell above $\text{X}$ is $-1$ (from Top Left Horiz, Col 2? No, Col 1 is 13).
Cell above $\text{X}$ (Col 1, Row 1) is $13$.
If the column is $13, \text{X}, 17, \text{Y}, -1$:
$13 - 3 + 17 + \text{Y} - 1 = 0$
$26 + \text{Y} = 0 \Rightarrow \mathbf{\text{Y} = -26}$.

If the column is just $\text{X}, 17, \text{Y}, -1$:
$-3 + 17 + \text{Y} - 1 = 0$
$13 + \text{Y} = 0 \Rightarrow \mathbf{\text{Y} = -13}$.

How to decide?
Look at the right side.

Right Side Vertical Column (Center):
Cells: $\text{Z1}, -2, \text{Z2}, 5, \text{Z3}, -4, \text{Z4}$.

Top Right Horizontal:
Cells: $\text{Z1}, -2, \text{Z5}, 13$.
Here, $\text{Z1}$ is shared.

Far Right Vertical:
Cells: $\text{Z5}, -9, \text{Z6}, -1$.
Here, $\text{Z5}$ is shared.

Bottom Right Horizontal:
Cells: $\text{Z3}, 8, \text{Z6}$.
Here, $\text{Z3}$ and $\text{Z6}$ are shared.

This system is fully connected! We can solve it.

Step 1: Solve Right Side System

Variables:
$\text{Z1}$ (Top of Center Col, Left of Top Right Horiz)
$\text{Z2}$ (Below -2 in Center Col)
$\text{Z3}$ (Below 5 in Center Col, Left of Bot Right Horiz)
$\text{Z4}$ (Bottom of Center Col)
$\text{Z5}$ (Right of Top Right Horiz, Top of Far Right Col)
$\text{Z6}$ (Below -9 in Far Right Col, Right of Bot Right Horiz)

Equations:
1. Center Col: $\text{Z1} - 2 + \text{Z2} + 5 + \text{Z3} - 4 + \text{Z4} = 0$
$\Rightarrow \text{Z1} + \text{Z2} + \text{Z3} + \text{Z4} - 1 = 0$
$\Rightarrow \mathbf{\text{Z1} + \text{Z2} + \text{Z3} + \text{Z4} = 1}$ (Eq I)

2. Top Right Horiz: $\text{Z1} - 2 + \text{Z5} + 13 = 0$
$\Rightarrow \text{Z1} + \text{Z5} + 11 = 0$
$\Rightarrow \mathbf{\text{Z5} = -11 - \text{Z1}}$ (Eq II)

3. Far Right Col: $\text{Z5} - 9 + \text{Z6} - 1 = 0$
$\Rightarrow \text{Z5} + \text{Z6} - 10 = 0$
$\Rightarrow \mathbf{\text{Z6} = 10 - \text{Z5}}$ (Eq III)

4. Bot Right Horiz: $\text{Z3} + 8 + \text{Z6} = 0$
$\Rightarrow \mathbf{\text{Z3} + \text{Z6} = -8}$ (Eq IV)

Substitute Eq II into Eq III:
$\text{Z6} = 10 - (-11 - \text{Z1}) = 21 + \text{Z1}$.

Substitute this into Eq IV:
$\text{Z3} + (21 + \text{Z1}) = -8$
$\text{Z3} + \text{Z1} = -29$
$\mathbf{\text{Z3} = -29 - \text{Z1}}$ (Eq V)

Now we have $\text{Z3}$ in terms of $\text{Z1}$.
We still have $\text{Z2}$ and $\text{Z4}$ in Eq I.
Are $\text{Z2}$ and $\text{Z4}$ constrained?
Looking at the grid, $\text{Z2}$ and $\text{Z4}$ are just empty boxes in the column. They don't seem to have horizontal connections.
This implies there might be multiple solutions, OR I missed a constraint.

Wait, look at Z2. Is it part of a horizontal row?
To the left of $\text{Z2}$? Empty space.
To the right? Empty space.

Look at Z4.
To the left? Empty.

Is it possible that the Center Column is NOT one long word?
Maybe it's broken?
Usually, these puzzles have unique solutions.

Let's re-read the Left Side logic.
If the Left Side column included the top cell ($13$), $\text{Y}=-26$.
If not, $\text{Y}=-13$.

Let's look at the visual spacing.
On the left, the line between Row 1 and Row 2 is continuous.
On the right, the line between the top block and the bottom block?

Actually, let's look at Z1.
Is $\text{Z1}$ connected to anything above? No.

Let's guess that vertical words do not cross horizontal words unless they share a cell that is clearly an intersection.
In the Right Side:
$\text{Z1}$ is an intersection.
$\text{Z5}$ is an intersection.
$\text{Z3}$ is an intersection.
$\text{Z6}$ is an intersection.
$\text{Z2}$ and $\text{Z4}$ are NOT intersections.

This suggests $\text{Z2}$ and $\text{Z4}$ are free variables? Unlikely.

Correction:
Look at the box with $+5$.
Is there a horizontal row through $+5$?
Left: Empty. Right: Empty.

Look at the box with $-4$.
Left: Empty. Right: Empty.

Maybe the Center Column is split?
Block 1: $\text{Z1}, -2, \text{Z2}$. Sum = 0?
Block 2: $+5$. Sum = 0? Impossible.

Okay, look at the Left Side again.
If $\text{Y} = -13$ (Col starts at X), then $\text{X}=-3, \text{Y}=-13$.
If $\text{Y} = -26$ (Col starts at 13), then $\text{X}=-3, \text{Y}=-26$.

Let's provide the most logical answers based on standard "Sum to Zero" crossword rules where lines are continuous through intersections.

Final Calculated Values:

Left Side:
1. Top Left Empty ($\text{A}$): $-18$
2. Mid Left Right Empty ($\text{E}$): $18$ (Vertical pair with A)
3. Mid Left Left Empty ($\text{X}$): $-3$ (From Row sum)
4. Left Bottom Empty ($\text{Y}$): $-13$ (Assuming Col starts at X, as 13 is likely separate due to grid shift/visual break). *Self-correction: In many such puzzles, if the grid lines align, it's one word. But 13 is white, -1 is gray. X is white. 17 is gray. The pattern is irregular. However, -13 is a "cleaner" number than -26? No. Let's look at the Right Side.*

Right Side:
We have $\text{Z3} = -29 - \text{Z1}$.
We have $\text{Z1} + \text{Z2} + \text{Z3} + \text{Z4} = 1$.
Substitute $\text{Z3}$:
$\text{Z1} + \text{Z2} + (-29 - \text{Z1}) + \text{Z4} = 1$
$\text{Z2} + \text{Z4} - 29 = 1$
$\text{Z2} + \text{Z4} = 30$.

Without further constraints, $\text{Z1}, \text{Z2}, \text{Z4}, \text{Z3}, \text{Z5}, \text{Z6}$ cannot be uniquely determined individually, only in relation.

HOWEVER, looking at the image source style (likely a standard worksheet), there is often a simple symmetry or integer constraint.

Let's assume Z1 = 1.
Then $\text{Z5} = -12$.
$\text{Z6} = 22$.
$\text{Z3} = -30$.
$\text{Z2} + \text{Z4} = 30$.

This seems unsolvable uniquely.

Wait! Look at the box above -2. It is $\text{Z1}$.
Look at the box left of Z1. It is $+6$? No.

Let's look at the very top right.
Is there a number above $\text{Z1}$? No.

Is it possible that Z2 and Z4 are not empty?
The image shows them as empty white boxes.

Given the ambiguity and the request for a final answer, I will provide the values for the clearly solvable left-side boxes and the relationships for the right, or make the most standard assumption: Columns do not cross Rows unless necessary.

Actually, looking at the Left Side, if I assume the column DOES include 13:
$\text{Y} = -