Puzzle Box addition worksheets - Math Worksheets - MathsDiary.com - Free Printable

Let's solve the Math Puzzle Boxes step by step.

---

🔍 Understanding the Rules:

- Each puzzle uses numbers from 21 to 29, inclusive.
- Numbers must not be repeated in a single puzzle (so each number can only appear once per grid).
- Each row and column must add up to the number shown outside the box.
- We need to fill in the missing numbers so that:
- Row sums match the totals on the right.
- Column sums match the totals at the bottom.
- All numbers used are between 21 and 29, with no repeats.

We’ll go through each of the 9 puzzles one by one.

---

## ✔ Puzzle 1 (Top Left) – Green Grid

```
| | | 74
----|---|---|----
23 | 25 | | 72
----|---|---|----
21 | | 28 | 79
----|---|---|----
76 | 69 | 80 |
```

We have:
- Given: 23, 25, 21, 28
- Missing: One number in top-right, middle-center, bottom-left

Let’s label positions:

```
A B C
D E F
G H I
```

Given:
- A = 23, B = 25, D = 21, F = 28, G = ? (but G is given as 76? Wait — no!)

Wait! The numbers outside are the sums.

So:
- Column 1 sum = 76 → A + D + G = 76
- Column 2 sum = 69 → B + E + H = 69
- Column 3 sum = 80 → C + F + I = 80
- Row 1 sum = 74 → A + B + C = 74
- Row 2 sum = 72 → D + E + F = 72
- Row 3 sum = 79 → G + H + I = 79

Given:
- A = 23, B = 25, D = 21, F = 28

Now let's solve:

Step 1: Row 1 sum = 74

A + B + C = 74
23 + 25 + C = 74 → C = 74 - 48 = 26

✔ So C = 26

Step 2: Row 2 sum = 72

D + E + F = 72
21 + E + 28 = 72 → E = 72 - 49 = 23

But 23 already exists in A. Can't repeat!

✘ Conflict! But wait — maybe we made a mistake?

Wait: Is 23 already used? Yes, A = 23.

So E = 23 would be duplicate → not allowed.

So contradiction?

Wait — let's double-check:

Row 2: D = 21, F = 28 → 21 + 28 = 49 → E = 72 - 49 = 23 → yes.

But 23 is already in A. So unless it's allowed to repeat? No — rule says: "without repeating any numbers."

So this means either the puzzle is invalid or we misread.

Wait — maybe each puzzle independently uses numbers 21–29 without repetition — meaning only one occurrence per puzzle.

So if 23 is already used, E cannot be 23.

But mathematically, E must be 23.

So contradiction → impossible?

Wait — let’s recheck all values.

Wait — look at the image again.

In Puzzle 1, the top-left green grid has:

```
23 25 | 74
21 | 72
28 | 79
76 69 80
```

So:
- Top row: 23, 25, ?
- Middle row: 21, ?, 28
- Bottom row: ?, ?, ?

And column sums: 76, 69, 80

Row sums: 74, 72, 79

So:
- Row 1: 23 + 25 + C = 74 → C = 74 - 48 = 26
- Row 2: 21 + E + 28 = 72 → E = 72 - 49 = 23
- But 23 is already in A → conflict!

So unless the same number can be used multiple times? But instructions say: "without repeating any numbers"

So likely, each puzzle uses distinct numbers from 21–29, i.e., exactly nine numbers, no duplicates.

So if 23 appears twice, it violates the rule.

Thus, this puzzle has a problem?

Wait — but maybe we’re misunderstanding the layout.

Wait — perhaps the numbers outside are the sums, and the inside boxes are to be filled.

But the given numbers may be part of the solution.

Wait — look again: the grid shows:

```
[23] [25] | 74
[21] [ ] [28] | 72
[ ] [ ] [ ] | 79
76 69 80
```

So:
- Box A1 = 23
- Box A2 = 25
- Box B1 = 21
- Box B3 = 28

So far, numbers used: 23, 25, 21, 28

So 21, 23, 25, 28 are used.

Now:

Row 1: 23 + 25 + C = 74 → C = 74 - 48 = 26 → C = 26 ✔

Now numbers used: 21, 23, 25, 26, 28

Row 2: 21 + E + 28 = 72 → E = 23 → ✘ 23 already used

So E = 23 → duplicate → not allowed.

So no solution possible?

But that can’t be — probably we’re misreading.

Wait — maybe the number 23 is not actually used twice?

Wait — could the 23 in A1 be different from the one in E? But they are both in the same puzzle.

Unless the puzzle allows reuse? But instructions say: “without repeating any numbers.”

So if the same number appears more than once in the same puzzle, it's invalid.

So unless there’s a typo.

Alternatively, maybe the numbers outside are clues, and the given numbers inside are fixed, and we must find others.

But here, the math forces E = 23, which is already used.

So this puzzle has no valid solution under the rules?

But that seems unlikely.

Wait — perhaps I misread the row sums.

Let’s check the image carefully.

The text says:

> Each puzzle contains the numbers 21-29. Each column and each row add up to the number given outside the boxes.

So each puzzle uses all numbers from 21 to 29? That’s 9 numbers.

But a 3x3 grid has 9 cells → so each number from 21 to 29 is used exactly once.

Ah! That’s key.

So each puzzle uses numbers 21–29 exactly once — no repeats, all numbers used.

So every number from 21 to 29 must appear exactly once in the grid.

That changes everything.

So for Puzzle 1, we must use all numbers 21–29.

Currently given:
- 23, 25, 21, 28

So used: 21, 23, 25, 28

Remaining: 22, 24, 26, 27, 29

Now:

Row 1: 23 + 25 + C = 74 → C = 74 - 48 = 26 → C = 26 ✔

Now used: 21,23,25,26,28

Remaining: 22,24,27,29

Row 2: 21 + E + 28 = 72 → E = 72 - 49 = 23 → but 23 is already used → ✘

Again, same issue.

So E = 23 → duplicate → invalid.

So impossible?

But that can't be.

Wait — unless the 23 in A1 is not actually part of the grid? But it is written in the box.

Maybe the given numbers are not fixed? But they are printed in the box.

Wait — perhaps the puzzle allows some numbers to be pre-filled, and others to be filled in, but still using only 21–29 without repeats.

But even then, if 23 is already used, and E must be 23, it's invalid.

So unless the sums are wrong, or the given numbers are wrong, this puzzle is unsolvable.

But let's check the sums.

Wait — let’s try to see if there’s a mistake in our interpretation.

Another idea: Maybe the "23" in the first cell is not a given number, but part of the clue?

No — it’s in a green box, like the others.

Wait — perhaps the grid is partially filled, and we must complete it.

But with E = 23 required, and 23 already used, it's impossible.

Unless the 23 in A1 is not the number 23, but something else?

No — it clearly says 23.

Wait — let's try Puzzle 2 instead — maybe it’s easier.

---

## ✔ Puzzle 2 (Top Middle) – Yellow Grid

```
| 29 | | 82
----|----|---|----
22 | 24 | | 67
----|----|---|----
26 | | | 76
----|----|---|----
73 | 77 | 75 |
```

Given:
- A1 = 22, A2 = 24, B1 = 26, A3 = 29

So numbers used: 22, 24, 26, 29

Sums:
- Col1: 73 → A1 + B1 + C1 = 22 + 26 + C1 = 48 + C1 = 73 → C1 = 25
- Col2: 77 → A2 + B2 + C2 = 24 + B2 + C2 = 77 → B2 + C2 = 53
- Col3: 75 → A3 + B3 + C3 = 29 + B3 + C3 = 75 → B3 + C3 = 46
- Row1: 82 → 22 + 24 + 29 = 75 → wait! 22+24+29 = 75 ≠ 82 → ✘

Oh! 22 + 24 + 29 = 75, but row sum is 82 → difference of 7.

So either the sum is wrong or the numbers are wrong.

But 22+24+29 = 75, but row sum is 82 → impossible.

So unless A3 is not 29?

But it is labeled 29.

Wait — perhaps the top-right cell is not 29?

Look at the image:

It says:

```
| 29 | | 82
----|----|---|----
22 | 24 | | 67
----|----|---|----
26 | | | 76
```

So top row: ?, 29, ? → sum = 82

But we don't know the leftmost cell.

So let's define:

Let:
- A1 = ?, A2 = 29, A3 = ?
- B1 = 22, B2 = 24, B3 = ?
- C1 = 26, C2 = ?, C3 = ?

Column sums:
- Col1: A1 + B1 + C1 = A1 + 22 + 26 = A1 + 48 = 73 → A1 = 25
- Col2: A2 + B2 + C2 = 29 + 24 + C2 = 53 + C2 = 77 → C2 = 24 → but 24 already used (B2) → ✘

C2 = 24, but 24 is already in B2 → duplicate → invalid.

So again, conflict.

This is problematic.

Wait — maybe the 24 in B2 is not fixed?

But it's in the box.

Perhaps the given numbers are not all fixed? But they are shaded.

Wait — perhaps only the shaded cells are given, and the others are to be filled.

But in Puzzle 2, A2=29, B1=22, B2=24, C1=26 are given.

So used: 22,24,26,29

From col1: A1 + 22 + 26 = 73 → A1 = 25

So now used: 22,24,25,26,29

Col2: 29 + 24 + C2 = 77 → C2 = 77 - 53 = 24 → 24 again → duplicate → invalid.

So again, impossible.

Wait — unless the sums are for the rows and columns, and we must accept that some numbers might be repeated? But instructions say "without repeating any numbers".

So this suggests either:
- The puzzle has errors, or
- Our understanding is wrong.

Wait — let's look at Puzzle 3.

---

## ✔ Puzzle 3 (Top Right) – Green Grid

```
28 | | | 74
----|---|---|----
23 | | | 78
----|---|---|----
21 | 27 | | 73
----|---|---|----
74 | 76 | 75 |
```

Given:
- A1 = 28, B1 = 23, C1 = 21, C2 = 27

Used: 21,23,27,28

Numbers available: 22,24,25,26,29

Sums:
- Col1: 28 + 23 + 21 = 72 → but sum is 74 → 72 ≠ 74 → difference of 2 → not matching.

Wait — col1 sum is 74, but current sum is 28+23+21 = 72 → so we need 74 → missing 2 → impossible.

So unless the bottom-left sum is 72, but it's labeled 74.

So conflict.

But the bottom of the grid says: 74, 76, 75

So col1 sum = 74, but current total = 72 → needs to be 74 → so sum of three numbers = 74.

But 28+23+21 = 72 → so if those are fixed, impossible.

So unless the 21 is not in C1?

But it is.

Wait — perhaps the given numbers are not all fixed? But they are in the box.

I think there’s a fundamental issue.

Wait — let’s try a different approach.

Maybe the numbers outside are the sums, and the given numbers inside are correct, and we need to fill in the rest, but the numbers 21–29 are used across the entire puzzle set, not per puzzle?

But the instruction says: "Each puzzle contains the numbers 21-29" — so likely per puzzle.

But then each puzzle must use all nine numbers 21–29 exactly once.

But in many cases, the sums don't add up.

For example, in Puzzle 3:

- Col1: 28 + 23 + 21 = 72, but sum is 74 → impossible.

So unless the 21 is not in C1.

But it is.

Wait — perhaps the 21 is in C2? No, it's in C1.

Wait — look at the image again.

In Puzzle 3:

```
[28] [ ] [ ] | 74
[23] [ ] [ ] | 78
[21] [27] [ ] | 73
74 76 75
```

So:
- A1 = 28
- B1 = 23
- C1 = 21
- C2 = 27

Sum of col1: 28 + 23 + 21 = 72, but should be 74 → so error.

So unless the sum is 72, but it's written as 74.

So likely, there is a typo in the puzzle.

Alternatively, maybe the numbers outside are not the sums, but something else.

Wait — the instruction says: "each column and each row add up to the number given outside the boxes"

So they are sums.

But then in this case, it's impossible.

Unless the given numbers are not fixed — but they are in the box.

Wait — perhaps the pre-filled numbers are hints, and we can change them? But that doesn't make sense.

Another possibility: The numbers 21–29 are used in the entire set of puzzles, not per puzzle.

But the instruction says: "Each puzzle contains the numbers 21-29" — so likely per puzzle.

But that would require 9 cells, 9 numbers — so yes.

But then the sums must be consistent.

Let’s try Puzzle 4.

---

## ✔ Puzzle 4 (Middle Left) – Yellow Grid

```
21 | | | 73
----|---|---|----
26 | 22 | | 73
----|---|---|----
| | | 79
----|---|---|----
79 | 69 | 77 |
```

Given:
- A1 = 21, B1 = 26, B2 = 22

Used: 21,22,26

Sums:
- Col1: 21 + 26 + C1 = 79 → C1 = 79 - 47 = 32 → but 32 > 29 → impossible.

So C1 = 32 → not in 21–29 → invalid.

So impossible.

This suggests that either the puzzle has typos, or our understanding is wrong.

Wait — perhaps the numbers outside are not the sums of the rows/columns, but something else.

But the instruction says: "each column and each row add up to the number given outside the boxes"

So they are sums.

But then in this case, col1 sum is 79, but 21+26+C1 = 79 → C1 = 32 → invalid.

So unless the sum is 47, but it's 79.

So clearly impossible.

This suggests that the puzzle might have errors, or we are misreading.

Wait — perhaps the numbers outside are not the totals, but the numbers to be placed?

No — the instruction says: "add up to the number given outside"

So they are totals.

Another possibility: The grid is 3x3, and the numbers outside are the sums, but the given numbers are not necessarily fixed.

But they are in the box.

Wait — perhaps the pre-filled numbers are the ones to be used, and we need to place the others.

But in Puzzle 4, A1=21, B1=26, B2=22

Then col1: 21 + 26 + C1 = 79 → C1 = 32 → impossible.

So no solution.

Unless the sum is 47, but it's 79.

So likely, the sums are incorrect or the given numbers are wrong.

But let's try Puzzle 5.

---

## ✔ Puzzle 5 (Middle Center) – Green Grid

```
27 | 21 | | 72
----|----|---|----
25 | | | 73
----|----|---|----
28 | | | 80
----|----|---|----
78 | 77 | 70 |
```

Given:
- A1 = 27, A2 = 21, B1 = 25, C1 = 28

Used: 21,25,27,28

Col1: 27 + 25 + 28 = 80 → but sum is 78 → 80 ≠ 78 → difference of 2 → not matching.

So impossible.

Wait — col1 sum is 78, but current sum is 80 → too high.

So unless the numbers are not fixed.

But they are.

This is very confusing.

Perhaps the numbers outside are not the sums, but the numbers to be placed in the corners?

But the instruction says: "add up to the number given outside"

So they are sums.

After checking several puzzles, it seems that many of them have inconsistencies.

But let’s try one that might work.

---

## ✔ Puzzle 6 (Middle Right) – Yellow Grid

```
22 | 23 | | 76
----|----|---|----
| 27 | | 70
----|----|---|----
| | | 79
----|----|---|----
76 | 73 | 76 |
```

Given:
- A1 = 22, A2 = 23, B2 = 27

Used: 22,23,27

Sums:
- Col1: 22 + B1 + C1 = 76
- Col2: 23 + 27 + C2 = 73 → 50 + C2 = 73 → C2 = 23 → but 23 already used → duplicate → invalid.

So again, impossible.

---

## ✔ Puzzle 7 (Bottom Left) – Green Grid

```
21 | | | 73
----|---|---|----
25 | | | 74
----|---|---|----
24 | | | 78
----|---|---|----
79 | 74 | 72 |
```

Given:
- A1 = 21, B1 = 25, C1 = 24

Used: 21,24,25

Col1: 21 + 25 + 24 = 70, but sum is 79 → needs 79 → missing 9 → impossible.

So no.

---

## ✔ Puzzle 8 (Bottom Middle) – Yellow Grid

```
29 | | | 77
----|---|---|----
| 27 | | 73
----|---|---|----
21 | | | 75
----|---|---|----
74 | 73 | 78 |
```

Given:
- A1 = 29, B2 = 27, C1 = 21

Used: 21,27,29

Col1: 29 + B1 + 21 = 74 → B1 = 74 - 50 = 24

So B1 = 24

Used: 21,24,27,29

Col2: A2 + 27 + C2 = 73 → A2 + C2 = 46

Col3: A3 + B3 + C3 = 78

Row1: 29 + A2 + A3 = 77 → A2 + A3 = 48

Row2: 24 + 27 + B3 = 73 → B3 = 73 - 51 = 22

So B3 = 22

Used: 21,22,24,27,29

Row3: 21 + C2 + C3 = 75 → C2 + C3 = 54

Now from earlier:
- A2 + C2 = 46
- A2 + A3 = 48
- C2 + C3 = 54

Available numbers: 23,25,26,28

Used: 21,22,24,27,29

So remaining: 23,25,26,28

Now:
- A2 + C2 = 46
- A2 + A3 = 48
- C2 + C3 = 54

Try combinations.

Possible pairs for A2 + C2 = 46:
- 23+23 → duplicate
- 25+21 → 21 used
- 26+20 → out of range
- 28+18 → no

So only possible: 23 and 23 → not allowed

Or 25+21 → 21 used

26+20 → no

28+18 → no

So no pair of unused numbers adds to 46.

23+23 = 46 → but duplicate

25+21 = 46 → 21 used

26+20 = 46 → 20 not in 21–29

28+18 = 46 → 18 not in range

So no solution.

So again, impossible.

---

## ✔ Puzzle 9 (Bottom Right) – Green Grid

```
22 | 26 | | 72
----|----|---|----
| | | 76
----|----|---|----
29 | | | 77
----|----|---|----
80 | 68 | 77 |
```

Given:
- A1 = 22, A2 = 26, C1 = 29

Used: 22,26,29

Col1: 22 + B1 + 29 = 80 → B1 = 80 - 51 = 29 → but 29 already used → duplicate → invalid.

So impossible.

---

🚫 Conclusion:

After analyzing all 9 puzzles, none of them seem to have a valid solution under the rules:
- Use numbers 21–29 exactly once per puzzle
- No repeats
- Rows and columns sum to given totals

In every case, either:
- The sums don't add up with the given numbers
- Or the required number is outside 21–29
- Or a number must be repeated

Therefore, it appears that the puzzle sheet has errors — either in the given numbers, the sums, or the layout.

---

🔧 Possible Fixes:

1. Check for typos in the image — perhaps the numbers or sums are misprinted.
2. Re-evaluate the rules: maybe "contains the numbers 21-29" means that these are the only numbers used, but not necessarily all used — but then it's not clear how many to use.
3. Maybe the numbers outside are not the sums, but something else — but the instruction says they are.

---

✔ Final Answer:

The puzzle as presented contains inconsistencies and appears to have errors. None of the individual puzzles can be solved with the given constraints (using numbers 21–29 exactly once, no repeats, and row/column sums matching the outside numbers).

Please verify the puzzle image for typos or provide clarification on the rules.

If you can share a clearer version or confirm the intended numbers, I’d be happy to help solve a corrected version.