Free Printable Missing Numbers Worksheets! (1-20) ⋆ The Hollydog Blog - Free Printable

Let's solve the problem step by step.

Problem:

We are given a 3x3 grid of circles, with some numbers filled in and others missing. The task is to write the missing numbers so that the sequence makes sense — likely counting in order from 1 to 9.

Here’s the current layout:

```
[1] [ ] [3]
[ ] [5] [ ]
[ ] [9] [ ]
```

We need to fill in the blanks so that the numbers go in order from 1 to 9.

---

Step 1: Identify the pattern

Since we see:
- 1, 3 → so missing 2
- 5, 7 → so missing 6
- 9 → next would be 10, but only up to 9

So it seems like the numbers are arranged in increasing order from 1 to 9.

Let’s look at the positions:

- Top row: 1, ?, 3 → must be 2 in the middle
- Middle row: ?, 5, ? → we know 4 and 6 come before and after 5
- Bottom row: ?, 9, ? → 8 and 10? But 10 is too big. So probably 8 and then 10 is not possible.

Wait — let’s list all numbers from 1 to 9:

1, 2, 3, 4, 5, 6, 7, 8, 9

Now, let’s map them into the grid based on position.

We already have:
- Position (1,1): 1
- Position (1,3): 3
- Position (2,2): 5
- Position (2,4): 7 → wait, (2,3) is 7
- Position (3,2): 9

So coordinates:
- Row 1: [1], [ ], [3]
- Row 2: [ ], [5], [7]
- Row 3: [ ], [9], [ ]

Now, let’s try to fill in the missing numbers.

We need to place: 2, 4, 6, 8

Let’s look at the sequence.

From top-left to bottom-right, maybe it's going in order?

Try filling in sequentially:

1. 1 → (1,1)
2. 2 → (1,2)
3. 3 → (1,3)
4. 4 → (2,1)
5. 5 → (2,2)
6. 6 → (2,3)
7. 7 → (2,3) → already has 7 → conflict!

Wait — (2,3) is already 7, so 6 should be before it.

But (2,2) is 5, (2,3) is 7 → so (2,2) = 5, (2,3) = 7 → missing 6

So (2,3) is 7 → so 6 must be somewhere else.

But (2,3) is 7 → so 6 must be in another blank.

Wait — we have:
- (1,1): 1
- (1,2): ?
- (1,3): 3
→ So (1,2) must be 2

Then:
- (2,1): ?
- (2,2): 5
- (2,3): 7
→ So between 5 and 7 is 6 → so (2,3) is 7, so 6 must be in (2,1)? No, because 6 comes after 5, before 7.

But (2,2) = 5, (2,3) = 7 → so where is 6?

It can't be in (2,1), since that's before 5.

Wait — maybe the numbers are not in row-major order.

Alternatively, perhaps the numbers are placed in order, but not necessarily left-to-right.

Let’s list what’s missing:

Used: 1, 3, 5, 7, 9
Missing: 2, 4, 6, 8

Now, let’s consider the positions:

Row 1: 1, ?, 3 → so the middle must be 2 → because 1, 2, 3

So (1,2) = 2

Now Row 2: ?, 5, 7 → so between 5 and 7 is 6 → but 6 is missing, and there’s a blank at (2,1) and (2,3)

(2,3) is already 7 → so 6 must be in (2,1)? But (2,1) is before 5, and 6 > 5 → can’t be.

Wait — unless the sequence isn't left to right.

But more likely, the grid is meant to show consecutive numbers in order.

Wait — maybe it's not sequential in rows, but just missing numbers in the number line.

Perhaps the numbers are supposed to be filled in such a way that each row or column increases?

But let's think differently.

Maybe it's a simple counting puzzle: fill in the numbers from 1 to 9 in order, placing them in the grid.

But we don’t know the order.

But look at the clues:

- First row: 1, ?, 3 → clearly, the missing number is 2
- Second row: ?, 5, 7 → so the missing number between 5 and 7 is 6 → but 6 is not in the same row as 5 and 7? Wait — (2,2)=5, (2,3)=7 → so (2,3) is 7 → so the number before 7 is 6 → so 6 should be in (2,1)? But (2,1) is before 5 → no.

Wait — unless the numbers are not in order per row.

Alternative idea: Maybe it's a number grid where each row is increasing, and we’re to fill in the missing numbers.

Let’s assume the numbers are arranged in increasing order across the grid, like a sequence.

We have:

- 1, 3 → so 2 is missing
- 5, 7 → so 6 is missing
- 9 → so 8 and 10? But 10 is too big.

So missing: 2, 4, 6, 8

Now, let’s look at the positions:

We have:
- (1,1): 1
- (1,2): ?
- (1,3): 3
→ So (1,2) must be 2

Now:
- (2,1): ?
- (2,2): 5
- (2,3): 7
→ So the numbers around here: 5 and 7 → so 6 is missing → must be in one of the blanks

But (2,1) is before (2,2) → so if the row is increasing, then (2,1) < 5 → so could be 4

Then (2,2) = 5, (2,3) = 7 → so (2,3) is 7 → so missing 6 → but 6 is not in this row → contradiction?

Unless 6 is in (3,1) or something.

Wait — perhaps the grid is meant to represent the numbers 1 through 9 in order, placed in the correct positions.

But we don’t have a clear path.

Alternative idea: Perhaps it’s a counting puzzle where the numbers are placed in order from left to right, top to bottom.

Let’s try that:

Position (1,1): 1 → OK
(1,2): ? → should be 2
(1,3): 3 → OK

So (1,2) = 2

Now (2,1): ? → should be 4
(2,2): 5 → OK
(2,3): 7 → but should be 6 → conflict! We expected 6, but got 7

So not sequential left to right.

But (2,3) is 7 → so 7 is placed early.

So maybe the sequence is not row-wise.

Another idea: Maybe the numbers are in order, but placed in the grid in a specific pattern.

Let’s list known values:

- 1 → (1,1)
- 3 → (1,3)
- 5 → (2,2)
- 7 → (2,3)
- 9 → (3,2)

So positions:

| | | |
|-----|-----|-----|
| 1 | ? | 3 |
| ? | 5 | 7 |
| ? | 9 | ? |

Now, the numbers 1 to 9 must be used once.

Used: 1, 3, 5, 7, 9
Missing: 2, 4, 6, 8

Now, let’s think about logical placements.

In the first row: 1, ?, 3 → so the middle must be 2 → because 1, 2, 3

So (1,2) = 2

Now second row: ?, 5, 7

So we have 5 and 7 → so 6 must be somewhere → but where?

If we assume the grid is increasing in some way, perhaps diagonally or by columns.

Look at column 1: (1,1)=1, (2,1)=?, (3,1)=? → so 1, ?, ?

Column 2: (1,2)=2, (2,2)=5, (3,2)=9 → so 2, 5, 9 → which is increasing: 2, 5, 9 → differences: +3, +4 → not arithmetic

But 2, 5, 9 → gap of 3, then 4 → not helpful.

Column 3: (1,3)=3, (2,3)=7, (3,3)=? → 3, 7, ? → so missing 8 or 9, but 9 is already used.

9 is in (3,2), so (3,3) could be 8 or 10 → 10 too big → so (3,3) = 8? But 8 not yet used.

But 8 is missing.

Wait — missing numbers: 2, 4, 6, 8

We’ve assigned (1,2) = 2

Now:

- (2,1): ?
- (3,1): ?
- (2,3): 7 → already set
- (3,3): ?

And (2,2)=5, (3,2)=9

Now, look at column 3: 3, 7, ? → so 3 to 7 is +4 → so next could be +4 → 11 → too big → or maybe not.

But 8 is missing → could (3,3) = 8?

Then column 3: 3, 7, 8 → 3 to 7 is +4, 7 to 8 is +1 → not consistent.

But maybe not required.

Back to row 2: ?, 5, 7 → so the numbers are 5 and 7 → so 6 must be in the blank → but which blank?

The blanks are (2,1) and (2,3) → but (2,3) is already 7 → so 6 cannot be there.

So 6 must be in (2,1)? But (2,1) is before 5 → so if the row is increasing, then (2,1) < 5 → so 6 > 5 → can’t be.

So 6 cannot be in (2,1) if the row is increasing.

But maybe the row is not increasing.

But let’s try to assign 6.

Where can 6 go?

Possible positions: (2,1), (3,1), (3,3)

But (2,1) is in row 2, col 1 → next to 5 and 7 → so if we want 6 to be between 5 and 7, it should be in (2,2) or (2,3), but both are taken.

(2,2)=5, (2,3)=7 → so 6 is missing → but no spot in that row.

Unless the grid is not ordered by rows.

Another idea: Maybe it's a magic square? But 1+2+3=6, not magic.

Or perhaps it's just a simple counting exercise.

Wait — maybe the numbers are meant to be filled in order, but the grid is not sequential.

But look: 1, 2, 3 are in the first row → so likely (1,2) = 2

Similarly, 5 and 7 are in the second row → so maybe (2,1) = 4, (2,2) = 5, (2,3) = 7 → but then 6 is missing → so where is 6?

Ah! There's no room for 6 in the second row.

Unless the numbers are not in order.

But that doesn't make sense.

Wait — perhaps the numbers are not in order, but the grid is meant to be filled with the missing numbers in the sequence 1 to 9.

Let’s list all numbers from 1 to 9:

1, 2, 3, 4, 5, 6, 7, 8, 9

We have: 1, 3, 5, 7, 9

So missing: 2, 4, 6, 8

Now, let’s look at the positions:

- (1,2): must be 2 → because 1, ?, 3 → so 2 is the only number between 1 and 3

So (1,2) = 2

Now, (2,1): ?
(2,3): 7 → already set
(3,1): ?
(3,3): ?

And (3,2) = 9

Now, what about 4?

Where can 4 go?

Options: (2,1), (3,1), (3,3)

Similarly, 6 and 8.

Now, look at column 1: (1,1)=1, (2,1)=?, (3,1)=?

So 1, ?, ? → could be 1, 4, 8 or 1, 2, 3 but 2 and 3 are used.

But 2 is in (1,2), 3 in (1,3)

So column 1: 1, ?, ? → could be 1, 4, 8 or 1, 6, 8 etc.

But let’s look at column 2: (1,2)=2, (2,2)=5, (3,2)=9

So 2, 5, 9 → increasing

Column 3: (1,3)=3, (2,3)=7, (3,3)=?

3, 7, ? → difference: +4, then ? → could be +4 → 11 → too big, or +1 → 8

8 is available.

So (3,3) = 8?

Then column 3: 3, 7, 8 → not arithmetic, but possible.

Now, missing numbers: 2 (assigned), 4, 6, 8

We have (3,3) = 8

Now, remaining: 4, 6

Blanks: (2,1), (3,1)

Now, row 3: (3,1)=?, (3,2)=9, (3,3)=8

So (3,1), 9, 8 → so (3,1) must be less than 9 and 8 → could be 4 or 6

But if (3,1) = 4, then row 3: 4, 9, 8 → not sorted

If (3,1) = 6, then 6, 9, 8 → still not sorted

But maybe not required.

Now, row 2: (2,1)=?, (2,2)=5, (2,3)=7

So if (2,1) = 4, then 4, 5, 7 → missing 6

But 6 is not in this row.

6 must be in (3,1) or (3,3)

(3,3) is 8 → so 6 must be in (3,1)

So (3,1) = 6

Then (2,1) = 4

Now check:

- (2,1) = 4
- (3,1) = 6
- (3,3) = 8

Now let’s write the full grid:

```
Row 1: 1, 2, 3
Row 2: 4, 5, 7
Row 3: 6, 9, 8
```

Now check if numbers 1-9 are used:

1,2,3,4,5,6,7,8,9 → yes

All present.

Now, is there any issue?

Look at row 3: 6, 9, 8 → not in order

But maybe not required.

Column 1: 1, 4, 6 → increasing

Column 2: 2, 5, 9 → increasing

Column 3: 3, 7, 8 → increasing

Diagonals: 1,5,8 → 1,5,8 → +4,+3 → not constant

But overall, it works.

Is there a better arrangement?

Could (3,3) be 6?

Then (3,1) = 4, (3,3) = 6 → but then (2,1) = ? → must be 4 or 6, but both used.

No.

So only possibility is:

- (1,2) = 2
- (2,1) = 4
- (3,1) = 6
- (3,3) = 8

And (2,3) = 7, (3,2) = 9

So final grid:

```
1 2 3
4 5 7
6 9 8
```

Now, check if any number is missing or repeated: 1,2,3,4,5,6,7,8,9 — all present.

So the missing numbers are:

- (1,2): 2
- (2,1): 4
- (3,1): 6
- (3,3): 8

But wait — the prompt says "Write The Missing Numbers!" — so we need to fill in the blanks.

There are four blanks:

1. (1,2) → 2
2. (2,1) → 4
3. (2,3) → already 7 → not blank
4. (3,1) → 6
5. (3,3) → 8

Wait — let's count the blanks:

- (1,2): blank → fill with 2
- (2,1): blank → fill with 4
- (2,3): already 7 → not blank
- (3,1): blank → fill with 6
- (3,3): blank → fill with 8

Yes.

So the missing numbers are: 2, 4, 6, 8

But we need to assign them to the correct positions.

So the solution is:

```
1 2 3
4 5 7
6 9 8
```

Now, is this the only possible solution?

Suppose we put 8 in (2,1) — then (2,1)=8, but then (2,2)=5, so 8>5, but it's to the left — might be ok, but then (3,1) must be 4 or 6, but 4 and 6 are missing.

But (3,1) and (3,3) are both blank.

But if (2,1)=8, then (3,1) could be 4 or 6.

But then (3,3) would be 6 or 4, but 6 is needed.

But also, (3,2)=9, so (3,3) must be less than 9, so 6 or 4 or 8, but 8 is used.

But let’s try:

- (2,1)=8
- (3,1)=4
- (3,3)=6

Then grid:

```
1 2 3
8 5 7
4 9 6
```

Numbers: 1,2,3,8,5,7,4,9,6 → all present.

But now, row 2: 8,5,7 → 8>5<7 → not increasing

Row 3: 4,9,6 → 4<9>6 → not sorted

But is it valid? The problem doesn’t say they must be sorted.

But the original hint "Write The Missing Numbers!" suggests just filling in the numbers 1 to 9, with no duplicates.

So multiple solutions possible?

But likely, the intended solution is the one where numbers are in order.

But in our first solution, we have:

- Row 1: 1,2,3 → good
- Row 2: 4,5,7 → missing 6
- Row 3: 6,9,8 → 6 and 8

But 6 is not in row 2.

But perhaps the intended solution is different.

Wait — maybe the numbers are meant to be in order across the grid.

But let’s look back.

Another possibility: perhaps the grid is meant to be filled in order: 1,2,3,4,5,6,7,8,9 in row-major order.

So:

- (1,1): 1
- (1,2): 2
- (1,3): 3
- (2,1): 4
- (2,2): 5
- (2,3): 6
- (3,1): 7
- (3,2): 8
- (3,3): 9

But in the image, (2,3) is 7, not 6, and (3,2) is 9, not 8.

So conflict.

Given that (2,3) is 7 and (3,2) is 9, we cannot have that.

So the only way is to accept that the numbers are not in row-major order.

Therefore, the solution must be:

- (1,2) = 2
- (2,1) = 4
- (3,1) = 6
- (3,3) = 8

Because:

- 1,2,3 in first row → so (1,2)=2
- Then 4,5,7 in second row → so (2,1)=4
- Then 6,9,8 in third row → so (3,1)=6, (3,3)=8

And 8 is missing, so it goes to (3,3)

Thus, the missing numbers are:

- Top middle: 2
- Middle left: 4
- Bottom left: 6
- Bottom right: 8

So final answer:

```
1 2 3
4 5 7
6 9 8
```

This uses all numbers 1–9 exactly once.

✔ Solution:

Fill in the blanks as follows:

- Circle in row 1, column 2: 2
- Circle in row 2, column 1: 4
- Circle in row 3, column 1: 6
- Circle in row 3, column 3: 8

Answer:
The missing numbers are 2, 4, 6, and 8, placed as shown above.