Printable math puzzles for kids - Free Printable

Let’s solve each grid step by step. We’ll fill in the blanks so that all rows and columns add up or subtract correctly as shown.

---

First Grid (Left Side):

We have:

Row 1:
6 + ___ = 14 → So, blank = 14 - 6 = 8

Row 2:
___ + ___ + ___ = ? (we don’t know yet — but we’ll use column info)

Row 3:
___ + 9 = 16 → So, first blank = 16 - 9 = 7

Column 1:
6 + ___ + ___ = 13 → We already have 6 from row 1, and 7 from row 3 → 6 + 7 = 13 → so middle blank must be 0? Wait — let’s check again.

Wait — actually, looking at the structure:

The grid is 3x3 with operations between cells.

Actually, let me re-read the layout carefully.

It looks like this:

Top row: [6] [+] [ ] [=] [14] → so 6 + x = 14 → x = 8

Middle row: [ ] [+] [ ] [+] [ ] → no total given? But below it says “= [ ]” for each column? Actually, looking at the bottom:

Bottom row: [13] [+] [ ] [=] [ ] → Hmm.

Wait — perhaps it's better to think of it as a magic square style where each row and column has an operation leading to a result.

Looking again:

Left grid:

Row 1: 6 + A = 14 → A = 8

Row 3: B + 9 = 16 → B = 7

Column 1: 6 + C + D = 13? No — wait, the bottom left says “13 + ...”

Actually, looking at the very bottom row: “13 + [ ] = [ ]” — that might be part of column 1?

Perhaps the grid is structured such that:

Each row ends with an equals sign and a number, meaning the whole row evaluates to that number.

Similarly, each column may evaluate downward.

But in the left grid:

Row 1: 6 + _ = 14 → so second cell is 8

Row 3: _ + 9 = 16 → so first cell is 7

Now Column 1: starts with 6, then some number, then 7, and below that it says “= 13”? Or is “13” the start of another row?

Wait — look at the bottom-left corner: it says “13 + [ ] = [ ]” — that seems to be Row 4? But there are only 3 rows drawn.

Actually, looking at the image description (even though I can't see it), based on standard puzzles like this, it’s likely a 3x3 grid where:

- Each row has an equation ending in a result.
- Each column also has an equation going down, ending in a result at the bottom.

So for Left Grid:

Rows:

Row 1: 6 + A = 14 → A = 8

Row 2: B + C + D = ? (but we don’t have a row total — instead, maybe the column totals are given at bottom)

Wait — at the bottom of left grid, under column 1: it says “= 13”, under column 2: “= [ ]”, under column 3: “= [ ]”

And then below that: “13 + [ ] = [ ]” — that might be separate? Or perhaps it’s indicating that column 1 sums to 13?

Let me assume:

In left grid:

Columns sum vertically to the numbers at the bottom.

So:

Column 1: 6 (row1) + X (row2) + Y (row3) = 13

But from row3: Y + 9 = 16 → Y = 7

So 6 + X + 7 = 13 → 13 + X = 13 → X = 0

Then row2: 0 + C + D = ? — but we don’t have a row total for row2. However, column 2 and 3 have their own totals.

Also, row1: 6 + 8 = 14 — good.

Row3: 7 + 9 = 16 — good.

Now column 2: top is 8 (from row1), middle is C, bottom is 9 (from row3). And at bottom of column 2, it should equal something — but in the diagram, under column 2, it says “= [ ]” — empty? Then below that, “13 + [ ] = [ ]” — perhaps that’s not part of the grid?

Wait — looking back at user input:

Left grid:

6 + [ ] = 14
+ + +
[ ] + [ ] + [ ]
= = =
13 + [ ] = [ ]

This suggests:

After the three rows, there is a fourth line: “13 + [ ] = [ ]” which might be using the column sums?

Actually, perhaps the “=” under each column means the vertical sum of that column.

So:

Column 1: 6 (row1 col1) + A (row2 col1) + B (row3 col1) = value shown at bottom of col1 → which is 13? But then it says “13 + [ ] = [ ]” — confusing.

Alternative interpretation: Maybe the bottom row “13 + [ ] = [ ]” is actually row 4, and the “=” above it are for columns.

Let me try to map positions.

Label the left grid cells as:

R1C1=6, R1C2=?, R1C3=? → but row1 is "6 + [ ] = 14" → so probably R1C1=6, operator+, R1C2=?, operator=, R1C3=14? That doesn’t make sense because 14 is the result.

Standard way: In such puzzles, each row is an equation: e.g., cell1 op cell2 = result_cell.

But here, row1 has three elements before "=": "6 + [ ] = 14" — so likely: 6 + X = 14, so X=8, and the "14" is the result, not a cell.

Similarly, row3: "[ ] + 9 = 16" → so Y + 9 = 16, Y=7.

Then the "+" signs in row2 suggest it's adding three numbers: A + B + C = ? but no result given.

Then the "=" under each column suggest that the sum of the column equals the number at the bottom.

For column 1: R1C1 + R2C1 + R3C1 = bottom_value

From above: R1C1=6, R3C1=7 (since Y=7), and bottom of col1 is 13? But then it says "13 + [ ] = [ ]" — perhaps the "13" is the sum of column 1, and then "13 + [ ] = [ ]" is a separate thing? Or maybe it's indicating that the sum of column 1 is 13, and similarly for others.

Assume that the numbers at the very bottom are the column sums.

So for left grid:

Column 1 sum = 13

Column 2 sum = ? (empty in diagram, but we can calculate)

Column 3 sum = ?

And then "13 + [ ] = [ ]" might be a red herring or part of another calculation.

But in the diagram, after the three rows, there is a line with "= = =" under the columns, and then below that "13 + [ ] = [ ]" — perhaps "13" is the sum of column 1, and then they want us to do 13 plus something.

To resolve, let's list what we know for left grid:

From row1: 6 + A = 14 → A = 8 → so R1C2 = 8

From row3: B + 9 = 16 → B = 7 → so R3C1 = 7

Now, if column 1 sum is 13, then R1C1 + R2C1 + R3C1 = 6 + C + 7 = 13 → 13 + C = 13 → C = 0 → so R2C1 = 0

Now row2: R2C1 + R2C2 + R2C3 = 0 + D + E = ? — but we don't have a row total for row2. However, we have column sums for col2 and col3.

What is the sum for column 2? The diagram shows under col2: "= [ ]" — empty, but then at the very bottom, "13 + [ ] = [ ]" — perhaps the first [ ] is for col2 sum, and the second for col3 sum? But it's written as "13 + [ ] = [ ]", which might mean 13 (col1 sum) plus col2 sum equals col3 sum? That could be.

Assume that the bottom line "13 + [ ] = [ ]" means: sum_col1 + sum_col2 = sum_col3

We have sum_col1 = 13

Let S2 = sum_col2, S3 = sum_col3

Then 13 + S2 = S3

Now, column 2: R1C2 + R2C2 + R3C2 = 8 + D + F = S2 (where F is R3C2, but R3C2 is 9? No, in row3, it's "[ ] + 9 = 16", so R3C1 + R3C2 = 16? Or is it R3C1 + 9 = 16, implying that the 9 is R3C2?

Let's clarify the grid layout.

Typically in such diagrams, the grid is:

Row 1: Cell1 Op Cell2 = Result1

But here, for row1: "6 + [ ] = 14" — so likely, the "14" is not a cell, but the result of the operation.

Similarly, row3: "[ ] + 9 = 16" — so the "9" is probably Cell2 of row3, and "16" is the result.

Then row2: "[ ] + [ ] + [ ]" — no result, so perhaps it's just the cells, and the results are only for rows 1 and 3, and columns have their own results at the bottom.

Moreover, the "+" in row2 between cells suggests addition of three numbers, but no total given, so probably the column sums are what matter.

Also, the "=" under each column indicate that the sum of the three cells in that column equals the number at the bottom of that column.

For left grid:

- Bottom of col1: 13

- Bottom of col2: ? (let's call it X)

- Bottom of col3: ? (call it Y)

And then "13 + [ ] = [ ]" — likely, this is saying 13 + X = Y, i.e., sum_col1 + sum_col2 = sum_col3

Now, let's define the cells:

Let me denote the grid as:

Col1 Col2 Col3
Row1: 6 A ? but row1 is "6 + A = 14", so probably the result is separate, so perhaps the grid has only two cells per row for the operation, but that doesn't match.

Another common format is that the grid includes the operators and results, but that would make it larger.

Perhaps it's a 3x3 grid of numbers, with operations between them, and the results are outside.

Looking at the right grid for clue.

Right grid:

20 - 12 = [ ]
+ + +
[ ] + [ ] + [ ]
25 - [ ] = 13
= = =
[ ] - [ ] = [ ]

Here, row1: 20 - 12 = ? → 8

Row3: 25 - B = 13 → B = 12

Column 1: 20 + C + 25 = ? at bottom

etc.

And at bottom: "[ ] - [ ] = [ ]" — likely the column sums minus something.

For right grid, let's solve it first as it might be clearer.

Right grid:

Row1: 20 - 12 = D → D = 8

Row3: 25 - E = 13 → E = 12

Now, the "+" in row2 suggests that row2 is adding three numbers: F + G + H = ? but no result given.

Then the "=" under columns suggest vertical sums.

Bottom of col1: ? , col2: ? , col3: ?

And then "[ ] - [ ] = [ ]" at bottom — likely, sum_col1 - sum_col2 = sum_col3 or something.

Assume that the bottom line is for the column sums.

So for right grid:

Let S1 = sum of col1 = 20 (R1C1) + F (R2C1) + 25 (R3C1) = 45 + F

S2 = sum of col2 = 12 (R1C2) + G (R2C2) + E (R3C2) = 12 + G + 12 = 24 + G (since E=12)

S3 = sum of col3 = D (R1C3) + H (R2C3) + 13 (R3C3)? No, in row3, "25 - [ ] = 13", so the 13 is the result, not a cell. This is messy.

Perhaps in row3, "25 - [ ] = 13", the "[ ]" is R3C2, and "13" is R3C3? But then it's not consistent.

Let's look at the structure again.

In both grids, the last row has an equation involving the column sums.

For left grid, after the three rows, there is " = = = " under the columns, and then "13 + [ ] = [ ]" — so likely, the "13" is the sum of column 1, the first [ ] is sum of column 2, and the second [ ] is sum of column 3, and 13 + sum2 = sum3.

Similarly for right grid, "[ ] - [ ] = [ ]" likely means sum1 - sum2 = sum3 or something.

Let's apply that to left grid.

Left grid:

From row1: 6 + A = 14 → A = 8 → so R1C2 = 8

From row3: B + 9 = 16 → B = 7 → so R3C1 = 7

Assume that the "9" in row3 is R3C2, so R3C2 = 9

Then row3: R3C1 + R3C2 = 7 + 9 = 16, which matches.

Now, for column 1: R1C1 + R2C1 + R3C1 = 6 + C + 7 = 13 + C

But at bottom of col1, it's given as 13? In the diagram, under col1, it says "= 13" or is "13" part of the bottom line?

In the user input: for left grid, after the three rows, it says "= = =" and then "13 + [ ] = [ ]" — so probably the "13" is not under col1, but is the first number in the bottom equation.

Perhaps the column sums are not given; instead, the bottom line uses the column sums.

Let me define:

Let P = sum of column 1 = R1C1 + R2C1 + R3C1 = 6 + C + 7 = 13 + C

Q = sum of column 2 = R1C2 + R2C2 + R3C2 = 8 + D + 9 = 17 + D

R = sum of column 3 = R1C3 + R2C3 + R3C3

But what are R1C3, R2C3, R3C3? In row1, "6 + [ ] = 14", so perhaps R1C3 is 14? But that would be unusual.

Perhaps the grid is only the numbers, and the operators and results are outside, but in the diagram, the results are included in the row.

Another idea: in such puzzles, the number after "=" in each row is the result of the row operation, and the number after "=" in each column is the result of the column operation.

For left grid:

Row 1: 6 + X = 14 → X = 8

Row 2: Y + Z + W = ? (no result given, so perhaps not used)

Row 3: V + 9 = 16 → V = 7

Then for columns:

Col 1: 6 + Y + V = 6 + Y + 7 = 13 + Y, and this should equal the number at bottom of col1, which is not specified, but in the bottom line, "13 + [ ] = [ ]" might be related.

Perhaps the "13" is the sum of col1, so 13 + Y = 13 → Y = 0

Then col2: 8 + Z + 9 = 17 + Z, and this should be the first [ ] in "13 + [ ] = [ ]"

Col3: X + W + 9? R3C3 is not defined. In row3, "V + 9 = 16", so if 9 is R3C2, then R3C3 is not used in row3 operation.

This is confusing.

Let's look at the right grid for insight.

Right grid:

Row1: 20 - 12 = A → A = 8

Row3: 25 - B = 13 → B = 12

Then the bottom line: "[ ] - [ ] = [ ]"

Also, the "+" in row2 suggests addition.

Assume that for columns, the sum is taken, and then the bottom line is an operation on the column sums.

For right grid, suppose:

Sum_col1 = 20 + C + 25 = 45 + C

Sum_col2 = 12 + D + B = 12 + D + 12 = 24 + D (since B=12)

Sum_col3 = A + E + 13? But 13 is the result of row3, not a cell.

In row3, "25 - B = 13", so if B is R3C2, then R3C3 might be 13, but that would mean the result is stored in the grid, which is possible.

Assume that in each row, the result is placed in the third cell.

For left grid row1: "6 + [ ] = 14" — so perhaps R1C1=6, R1C2=8, R1C3=14

But then row1 is 6 + 8 = 14, good.

Row3: "[ ] + 9 = 16" — so R3C1=7, R3C2=9, R3C3=16

Then row2: "[ ] + [ ] + [ ]" — so R2C1, R2C2, R2C3, and no result, so perhaps the sum is not given, but for columns, the sum of the three cells equals the number at the bottom.

For left grid, at bottom, under col1: "= 13" — but 6 + R2C1 + 7 = 13 + R2C1, set equal to 13? Then R2C1=0

Under col2: "= [ ]" — 8 + R2C2 + 9 = 17 + R2C2

Under col3: "= [ ]" — 14 + R2C3 + 16 = 30 + R2C3

Then the bottom line "13 + [ ] = [ ]" — likely, 13 (sum col1) + sum col2 = sum col3

So 13 + (17 + R2C2) = 30 + R2C3

30 + R2C2 = 30 + R2C3 → R2C2 = R2C3

But we have no other constraint, so many solutions.

However, in row2, it's " [ ] + [ ] + [ ] " with no result, so perhaps the sum of row2 is not constrained, but we need to find specific values.

Perhaps the " + " in row2 means that the three cells are added, and the result is implied or something.

Another thought: in some puzzles, the grid is to be filled so that all row equations and column equations are satisfied, and the bottom line is additional.

For left grid, we have:

From row1: R1C2 = 8

From row3: R3C1 = 7, and if R3C2 = 9, then R3C3 = 16 (if the result is stored)

Then for col1: R1C1 + R2C1 + R3C1 = 6 + R2C1 + 7 = 13 + R2C1

If this equals the number at bottom of col1, which is not specified, but in the bottom line, "13" might be this sum, so 13 + R2C1 = 13 → R2C1 = 0

Then for col2: R1C2 + R2C2 + R3C2 = 8 + R2C2 + 9 = 17 + R2C2

For col3: R1C3 + R2C3 + R3C3 = 14 + R2C3 + 16 = 30 + R2C3

Then the bottom line "13 + [ ] = [ ]" — if [ ] for col2 sum and [ ] for col3 sum, then 13 + (17 + R2C2) = 30 + R2C3

30 + R2C2 = 30 + R2C3 → R2C2 = R2C3

Now, for row2: R2C1 + R2C2 + R2C3 = 0 + R2C2 + R2C3 = 2 * R2C2 (since R2C2 = R2C3)

But no constraint on this sum, so we can choose R2C2 = k, R2C3 = k for any k, but probably there's more.

Perhaps the " + " in row2 means that the sum is to be calculated, but no target, so maybe it's not used, or perhaps the grid is to be filled with single digits or something.

Maybe for row2, the sum is not given, but in the context, we can leave it, but the problem asks to solve, so likely there's a unique solution.

Let's look at the right grid.

Right grid:

Row1: 20 - 12 = 8, so if R1C3 = 8

Row3: 25 - B = 13, so B = 12, and if R3C3 = 13

Then R3C2 = B = 12

R1C1 = 20, R1C2 = 12, R1C3 = 8

R3C1 = 25, R3C2 = 12, R3C3 = 13

Then col1: 20 + R2C1 + 25 = 45 + R2C1

Col2: 12 + R2C2 + 12 = 24 + R2C2

Col3: 8 + R2C3 + 13 = 21 + R2C3

Bottom line: "[ ] - [ ] = [ ]" — likely sum_col1 - sum_col2 = sum_col3 or something.

Suppose sum_col1 - sum_col2 = sum_col3

Then (45 + R2C1) - (24 + R2C2) = 21 + R2C3

21 + R2C1 - R2C2 = 21 + R2C3

So R2C1 - R2C2 = R2C3

Also, for row2: R2C1 + R2C2 + R2C3 = ? no constraint.

Still underdetermined.

Perhaps the " + " in row2 for right grid means that the sum is to be used, but no target.

Another idea: in both grids, the bottom line is an equation involving the column sums, and for left grid, "13 + S2 = S3", and for right grid, "S1 - S2 = S3" or similar.

For left grid, from earlier, if we assume that the sum of col1 is 13, then from 6 + R2C1 + 7 = 13, so R2C1 = 0

Then S2 = 8 + R2C2 + 9 = 17 + R2C2

S3 = 14 + R2C3 + 16 = 30 + R2C3

Then 13 + S2 = S3 → 13 + 17 + R2C2 = 30 + R2C3 → 30 + R2C2 = 30 + R2C3 → R2C2 = R2C3

Now, for row2: 0 + R2C2 + R2C3 = 2 * R2C2

But no constraint, so perhaps we can set R2C2 = 0, R2C3 = 0, but then S2 = 17, S3 = 30, and 13 + 17 = 30, good.

Or R2C2 = 1, R2C3 = 1, S2=18, S3=31, 13+18=31, also good.

So not unique.

Unless there's a constraint that all numbers are non-negative integers, but still many solutions.

Perhaps the " + " in row2 means that the sum is the same as something else.

Let's read the user input again.

For left grid:

6 + [ ] = 14
+ + +
[ ] + [ ] + [ ]
= = =
13 + [ ] = [ ]

The " + " in the second row might indicate that the three cells are to be added, and the result is not given, but perhaps it's equal to the sum of the first row or something.

First row sum: 6 + 8 + 14 = 28? But 14 is the result, not a cell.

Perhaps only the left two cells are operands, and the right is result, so for row1, cells are 6 and 8, result 14.

For row3, cells 7 and 9, result 16.

For row2, three cells, no result, so perhaps the sum of the three cells is to be found, but not given.

Then for columns, the sum of the three cells in the column equals the number at the bottom.

For col1: cells R1C1=6, R2C1, R3C1=7, sum = 13 + R2C1, and this should equal the number at bottom of col1, which is not specified, but in the bottom line, "13" might be this sum, so 13 + R2C1 = 13 → R2C1 = 0

Then for col2: R1C2=8, R2C2, R3C2=9, sum = 17 + R2C2, and this is the first [ ] in "13 + [ ] = [ ]"

For col3: R1C3=14, R2C3, R3C3=16, sum = 30 + R2C3, and this is the second [ ]

Then 13 + (17 + R2C2) = 30 + R2C3 → 30 + R2C2 = 30 + R2C3 → R2C2 = R2C3

Now, for row2: R2C1 + R2C2 + R2C3 = 0 + R2C2 + R2C3 = 2 * R2C2

But no constraint, so perhaps the puzzle expects us to realize that R2C2 and R2C3 can be anything, but that can't be.

Perhaps the " + " in row2 means that the sum is 0 or something, but unlikely.

Another possibility: in the bottom line "13 + [ ] = [ ]", the "13" is not the sum of col1, but the number 13 from the bottom-left, and it's part of a new row.

Look at the bottom-left: "13 + [ ] = [ ]" — and above it, under col1, "= " , so perhaps the "13" is R4C1, and then " + [ ] = [ ]" is R4C2 and R4C3.

So for left grid, there is a fourth row: 13 + P = Q

And the "= = =" under the columns mean that the sum of the four cells in each column equals something, but that might be complicated.

Perhaps the "= = =" are for the first three rows, and the bottom line is separate.

Let's try to solve the right grid first, as it might be easier.

Right grid:

20 - 12 = [ ] → 8

+ + +
[ ] + [ ] + [ ]
25 - [ ] = 13 → so 25 - B = 13, B=12

= = =
[ ] - [ ] = [ ]

Assume that the result of each row is in the third cell.

So R1C3 = 8

R3C3 = 13

R3C2 = B = 12 (since 25 - 12 = 13)

R1C1 = 20, R1C2 = 12, R1C3 = 8

R3C1 = 25, R3C2 = 12, R3C3 = 13

Then for col1: R1C1 + R2C1 + R3C1 = 20 + C + 25 = 45 + C

Col2: 12 + D + 12 = 24 + D

Col3: 8 + E + 13 = 21 + E

Then the bottom line: "[ ] - [ ] = [ ]" — likely, sum_col1 - sum_col2 = sum_col3 or sum_col1 - sum_col3 = sum_col2, etc.

Suppose sum_col1 - sum_col2 = sum_col3

Then (45 + C) - (24 + D) = 21 + E

21 + C - D = 21 + E

So C - D = E

Also, for row2: C + D + E = ? no constraint.

Still underdetermined.

Perhaps the " + " in row2 means that the sum is to be equal to the sum of row1 or something.

Sum of row1 cells: 20 + 12 + 8 = 40

Sum of row3 cells: 25 + 12 + 13 = 50

Not helpful.

Another idea: in the bottom line, "[ ] - [ ] = [ ]" , the [ ] are the column sums, and for right grid, it might be sum_col1 - sum_col2 = sum_col3

So (45 + C) - (24 + D) = 21 + E

As above, C - D = E

Now, if we assume that the grid is to be filled with reasonable numbers, perhaps C,D,E are small.

But still not unique.

Perhaps for row2, the sum C + D + E is given by the context, but not.

Let's look back at the left grid.

In left grid, if we assume that the sum of col1 is 13, then R2C1 = 0

Then S2 = 8 + D + 9 = 17 + D

S3 = 14 + E + 16 = 30 + E

Then 13 + S2 = S3 → 13 + 17 + D = 30 + E → 30 + D = 30 + E → D = E

Then for row2: 0 + D + E = 2D

No constraint.

But perhaps in the bottom line "13 + [ ] = [ ]", the [ ] are to be filled, and for the grid, we need to provide the missing numbers in the grid, not the sums.

The task is to fill in the blanks in the grid, not the sums at the bottom.

In the left grid, the blanks are:

- In row1: one blank (after 6+)

- In row2: three blanks

- In row3: one blank (before +9)

- In the bottom line: two blanks in "13 + [ ] = [ ]"

Similarly for right grid.

For left grid, from row1: 6 + A = 14 → A = 8

From row3: B + 9 = 16 → B = 7

Then for row2: C + D + E = ? no target, so perhaps it's not constrained, but then the column sums will determine.

Perhaps the "= = =" under the columns mean that the sum of the three cells in the column equals the number at the bottom, and for col1, it's 13, so 6 + C + 7 = 13 → C = 0

For col2: 8 + D + 9 = S2, and S2 is the first [ ] in "13 + [ ] = [ ]"

For col3: 14 + E + 16 = S3, and S3 is the second [ ]

Then 13 + S2 = S3

As before, 13 + (8 + D + 9) = 14 + E + 16

13 + 17 + D = 30 + E

30 + D = 30 + E → D = E

So D and E are equal, but can be any number.

However, perhaps in the context of the puzzle, we can choose D = E = 0, or 1, but likely there's a specific value intended.

Perhaps the " + " in row2 means that the sum is 0, but 0+0+0=0, then S2 = 8+0+9=17, S3=14+0+16=30, 13+17=30, good.

Or if D=E=1, S2=18, S3=31, 13+18=31, also good.

So not unique.

Unless the grid is to be filled with positive integers, and perhaps minimize or something, but not specified.

Perhaps for row2, the sum is not important, and we can leave D and E as variables, but the problem asks to solve, so likely there's a unique solution.

Let's consider that in the bottom line "13 + [ ] = [ ]", the [ ] are to be filled, and for the grid, the only blanks are the ones in the rows, and the bottom line is part of the answer.

But still.

Another approach: perhaps the " = " under the columns are for the sum of the column, and for left grid, col1 sum is 13, col2 sum is say X, col3 sum is Y, and 13 + X = Y, and we have to find the grid cells.

From earlier, with R2C1 = 0, R2C2 = D, R2C3 = E, with D = E.

Then the grid is:

Row1: 6, 8, 14

Row2: 0, D, E

Row3: 7, 9, 16

With D = E.

Then the bottom line: 13 + (8+ D +9) = (14 + E +16) → 13 + 17 + D = 30 + E → 30 + D = 30 + E → D=E, good.

To have a specific answer, perhaps D and E are 0, as the simplest.

Or perhaps from the right grid, we can infer.

Let's solve the right grid similarly.

Right grid:

Row1: 20, 12, 8 (since 20-12=8)

Row3: 25, 12, 13 (since 25-12=13)

Then col1: 20 + C + 25 = 45 + C

Col2: 12 + D + 12 = 24 + D

Col3: 8 + E + 13 = 21 + E

Bottom line: "[ ] - [ ] = [ ]" — suppose it's sum_col1 - sum_col2 = sum_col3

Then (45 + C) - (24 + D) = 21 + E

21 + C - D = 21 + E

So C - D = E

Also, for row2: C + D + E = C + D + (C - D) = 2C

No constraint.

Again, not unique.

Perhaps for right grid, the bottom line is sum_col1 - sum_col3 = sum_col2 or something.

Suppose sum_col1 - sum_col3 = sum_col2

Then (45 + C) - (21 + E) = 24 + D

24 + C - E = 24 + D

So C - E = D

Same as before.

Or sum_col2 - sum_col1 = sum_col3, etc.

Perhaps it's sum_col1 - sum_col2 = the number in the bottom left, but not specified.

Another idea: in the bottom line for right grid, "[ ] - [ ] = [ ]", the [ ] are the results of the column sums, and for the grid, we need to fill the cells, and the bottom line is to be completed with the sums.

But still.

Perhaps for both grids, the row2 sum is equal to the sum of the first row or something.

For left grid, sum of row1 cells: 6 + 8 + 14 = 28

Sum of row3 cells: 7 + 9 + 16 = 32

Average or something.

Perhaps the product or other, but unlikely.

Let's calculate the difference.

Notice that in left grid, row1: 6+8=14, row3: 7+9=16, so the sum of the two operands is the result.

For row2, if it's C + D + E = S, but no S given.

Perhaps the " + " in row2 means that it's adding three numbers, and the result is the sum of the column sums or something.

I recall that in some puzzles, the grid is a magic square variant, but here it's not.

Perhaps the bottom line "13 + [ ] = [ ]" for left grid is to be interpreted as the sum of col1 is 13, sum of col2 is X, sum of col3 is Y, and 13 + X = Y, and we have to find X and Y, but the task is to fill the grid blanks.

The user said "solve the problem accurately", and "fill in the blanks".

In the left grid, the blanks are:

- Row1: one blank (between + and =) → we have 8

- Row2: three blanks

- Row3: one blank (before +9) → we have 7

- Bottom line: two blanks in "13 + [ ] = [ ]"

Similarly for right grid.

For left grid, with R2C1 = 0, and R2C2 = D, R2C3 = E, with D = E, and no other constraint, perhaps the intended answer is D = E = 0, as the simplest.

Then for bottom line, S2 = 8+0+9=17, S3=14+0+16=30, so 13 + 17 = 30

So the bottom line is 13 + 17 = 30

For right grid, similarly, if we assume sum_col1 - sum_col2 = sum_col3, and C - D = E, and if we set C=0, then E = -D, but negative may not be desired.

Set D=0, then E = C, from C - 0 = E, so E=C

Then sum_col1 = 45 + C

sum_col2 = 24 + 0 = 24

sum_col3 = 21 + C

Then sum_col1 - sum_col2 = (45+C) - 24 = 21 + C = sum_col3, good.

So for any C, it works.

If we set C=0, then E=0, D=0

Then grid:

Row1: 20, 12, 8

Row2: 0, 0, 0

Row3: 25, 12, 13

Then sum_col1 = 20+0+25=45

sum_col2 = 12+0+12=24

sum_col3 = 8+0+13=21

Then bottom line: 45 - 24 = 21, which is true.

So for right grid, with C=D=E=0, it works.

Similarly for left grid, with D=E=0, it works.

So perhaps that's the intended solution.

For left grid:

Grid:
6 + 8 = 14
0 + 0 + 0 = ? (not given, but ok)
7 + 9 = 16
Then column sums: col1: 6+0+7=13, col2: 8+0+9=17, col3: 14+0+16=30
Bottom line: 13 + 17 = 30

For right grid:
20 - 12 = 8
0 + 0 + 0 = ?
25 - 12 = 13
Column sums: col1: 20+0+25=45, col2: 12+0+12=24, col3: 8+0+13=21
Bottom line: 45 - 24 = 21

Perfect.

So the filled grids are:

Left grid:
6 + 8 = 14
0 + 0 + 0 = (