Fill in the missing numbers in the number puzzles.

Let's solve the puzzle step by step.

We are given two grids with missing numbers. The goal is to fill in the missing numbers such that the pattern or relationship between the numbers makes sense. Based on the layout, it looks like a cross-shaped grid, and the numbers likely follow a pattern based on addition or subtraction, possibly forming a sequence where adjacent numbers relate through arithmetic operations.

---

🔹 First Grid:

```
[ ] 113 [ ]
122 [ ] [ ]
132 [ ] [ ]
[ ] 144 [ ]
153
```

Let’s label the positions for clarity:

```
A 113 B
122 C D
132 E F
G 144 H
153
```

We can see:
- 113 is at the top center.
- 122 is left of center in row 2.
- 132 is left of center in row 3.
- 144 is center in row 4.
- 153 is bottom center.

Let’s look for patterns.

#### Step 1: Vertical column (center)
Look at the central vertical line:
- Row 1: 113
- Row 2: ?
- Row 3: ?
- Row 4: 144
- Row 5: 153

Wait — 144 and 153 are consecutive in this column? But there's a gap.

Actually, let's recheck the structure. It seems like the center column goes:
- Top: 113
- Then below it: ? (C), then ? (E), then 144, then 153?

But 144 and 153 are not directly aligned vertically unless the center column is:

- Row 1: 113
- Row 2: C
- Row 3: E
- Row 4: 144
- Row 5: 153

So we have:
- 113 → C → E → 144 → 153

Now, check if there's an arithmetic progression.

From 144 to 153: difference = +9
If consistent, maybe each step is +9?

Then:
- E = 144 - 9 = 135
- C = 135 - 9 = 126
- 113 → 126? That’s +13 — not consistent.

Alternatively, maybe the vertical column increases by 10s or 11s?

Try differences:
- 144 to 153: +9
- Suppose E = 135 → 144: +9
- C = 126 → E = 135: +9
- 113 → C = 126: +13 → not consistent.

Alternative idea: Maybe the horizontal lines are sequences.

Look at the left column:
- 122
- 132
- ?
- ?

From 122 to 132: +10

So perhaps the next number down is 142, then 152?

But below 132 is G, and below that is nothing? Wait, no — G is below 132, and below G is nothing, but 153 is at the very bottom center.

Wait — actually, the structure may be:

```
[A] 113 [B]
122 [C] [D]
132 [E] [F]
[G] 144 [H]
153
```

So the center column is:
- Row 1: 113
- Row 2: C
- Row 3: E
- Row 4: 144
- Row 5: 153

So:
- From 144 to 153: +9
- So maybe E = 144 - 9 = 135
- C = 135 - 9 = 126
- Then 113 → C = 126 → +13 → inconsistent.

Alternatively, maybe the diagonals or adjacent cells form sequences.

Another idea: Look at the left side:
- 122 (row 2)
- 132 (row 3)
- G (row 4)
- ? (but no more)

Difference: 132 - 122 = 10 → so G = 132 + 10 = 142?

Then below G would be... but no cell. But 153 is at bottom center.

Wait — maybe the bottom center is 153, and above it is 144, so 144 → 153 = +9.

So maybe the center column is:
- 113
- ?
- ?
- 144
- 153

Let’s suppose the center column increases by 9 per step from bottom up:
- 153
- 144 (diff: -9)
- So previous: 144 - 9 = 135
- Then: 135 - 9 = 126
- Then: 126 - 9 = 117
- But we have 113 at the top — not matching.

Wait, 113 vs 117 → off by 4.

Not good.

What if the center column has:
- 113
- C
- E
- 144
- 153

And we know 144 → 153 = +9

Suppose the pattern is +9 every time downward.

Then:
- E = 144 - 9 = 135
- C = 135 - 9 = 126
- Then 113 → C = 126 → +13 → not consistent.

But 122 and 132 are on the left.

122 → 132 = +10

So perhaps the left column is increasing by 10:
- 122
- 132
- G = 142
- Then below? No cell.

But 142 is just below 132.

Now, what about the right side?
We have:
- 113 at top
- D and F and H

No numbers yet.

But look at 144 and 153 — both in the center column.

Maybe the central cross is:
- Horizontal: 113, ?, ?
- Vertical: 122, ?, 132, ?, 144, 153

Wait — 122 and 132 are not on the same column.

Wait, better to draw it clearly.

Let me reconstruct the first grid as a cross:

```
[ ] 113 [ ]
122 [ ] [ ]
132 [ ] [ ]
[ ] 144 [ ]
153
```

So positions:

Row 1: A 113 B
Row 2: 122 C D
Row 3: 132 E F
Row 4: G 144 H
Row 5: 153

Now, the center column (middle column) is:
- Row 1: 113
- Row 2: C
- Row 3: E
- Row 4: 144
- Row 5: 153

So:
- 144 → 153: +9
- So perhaps E = 144 - 9 = 135
- C = 135 - 9 = 126
- Then 113 → C = 126 → +13 → not +9 → doesn't fit.

But maybe the vertical column from top to bottom is:
113 → C → E → 144 → 153

Assume equal steps? Let's see how many steps:
- 113 to 153 is 40 apart over 4 intervals? 113 → C → E → 144 → 153 → 4 steps.

153 - 113 = 40 → average increase of 10 per step.

But:
- 144 - 113 = 31 → over 3 steps → ~10.33 per step.

But 144 to 153 is only +9.

Not consistent.

Alternative idea: The numbers are increasing diagonally or in sequences.

Look at 122, 132, 144, 153 — these are in different rows.

Wait — 122 and 132 are in the left column, one below the other.

122 → 132 = +10

Then next down: G = 142?

Then below G? Nothing.

But 144 is in the center, row 4.

So maybe G = 142, and 144 is to its right.

So G = 142, 144 → difference +2.

Then H = ? → maybe 146?

But 153 is below 144.

144 → 153 = +9

So maybe the center column goes:
- 113
- C
- E
- 144
- 153

Let’s suppose the center column increases by 11 each time?

113 → C → E → 144 → 153

144 to 153 = +9 → not 11.

Try: 113 → 124 → 135 → 146 → 157 → too big.

No.

Wait — maybe the numbers are related to their neighbors via sums or differences.

Another idea: Perhaps the sum of adjacent numbers or difference is constant.

But let's try looking at the second grid — maybe it's easier.

---

🔹 Second Grid:

```
[ ] 308 [ ]
317 319 321
[ ] 328 [ ]
[ ] 348 [ ]
```

Let’s label:

```
A 308 B
317 319 321
C 328 D
E 348 F
```

Now observe:

- The top row: A, 308, B
- Middle row: 317, 319, 321
- Next: C, 328, D
- Bottom: E, 348, F

Look at the center column:
- 308
- 319
- 328
- 348

Check differences:
- 308 → 319 = +11
- 319 → 328 = +9
- 328 → 348 = +20 → not consistent.

But wait — 308, 319, 328, 348 — not arithmetic.

But look at the middle row: 317, 319, 321 → increasing by 2!

So it's an arithmetic sequence: +2 each.

Similarly, top row: A, 308, B — probably also +2?

So if 308 is middle, then:
- A = 308 - 2 = 306
- B = 308 + 2 = 310

Similarly, third row: C, 328, D

If same pattern, then:
- C = 328 - 2 = 326
- D = 328 + 2 = 330

Fourth row: E, 348, F → likely:
- E = 348 - 2 = 346
- F = 348 + 2 = 350

Now, check vertical columns.

Left column:
- A = 306
- 317
- C = 326
- E = 346

Check differences:
- 306 → 317 = +11
- 317 → 326 = +9
- 326 → 346 = +20 → not consistent.

But look at center column again:
- 308
- 319
- 328
- 348

Now:
- 308 → 319 = +11
- 319 → 328 = +9
- 328 → 348 = +20 → still not clear.

Wait — maybe the center column is increasing by 11, then 9, then 20 — no.

But notice:
- 317, 319, 321 — middle row: +2
- 308, 319, 328, 348 — center column

Wait — 319 is both in middle row and center column.

So maybe the center column is increasing by 11, then 9, then 20 — not helpful.

But look at vertical changes.

Left column:
- 306 (A)
- 317
- 326 (C)
- 346 (E)

Differences:
- 306 → 317 = +11
- 317 → 326 = +9
- 326 → 346 = +20 → not nice.

But 306 → 317 = +11, 317 → 326 = +9 → decreasing by 2?

Then 326 → 346 = +20 → jump.

Not good.

Alternative idea: Maybe the grid is built so that each number is the average of its neighbors, but unlikely.

Wait — another possibility: Each row is an arithmetic sequence.

We already assumed that.

So:
- Row 1: A=306, 308, B=310 → +2
- Row 2: 317, 319, 321 → +2
- Row 3: C=326, 328, D=330 → +2
- Row 4: E=346, 348, F=350 → +2

That makes sense.

Now check columns.

Center column:
- 308
- 319
- 328
- 348

Differences:
- 308 → 319 = +11
- 319 → 328 = +9
- 328 → 348 = +20 → not consistent.

But wait — maybe not required to be consistent.

But now look at left column:
- 306
- 317
- 326
- 346

Differences:
- 306 → 317 = +11
- 317 → 326 = +9
- 326 → 346 = +20 → still not good.

But 306 to 317: +11, 317 to 326: +9, 326 to 346: +20 — no pattern.

Wait — maybe the left column increases by 11, then 9, then 20 — not useful.

But look at the right column:
- B = 310
- 321
- D = 330
- F = 350

Differences:
- 310 → 321 = +11
- 321 → 330 = +9
- 330 → 350 = +20 → same pattern.

So all columns have:
- First: +11, +9, +20
- Second: +11, +9, +20
- Third: +11, +9, +20

So maybe the column increases by +11, then +9, then +20?

But why?

Wait — maybe the rows are +2, and columns have a fixed pattern.

But let's go back to the first grid.

---

🔹 Back to First Grid

Let’s assume that the same pattern applies: each row is an arithmetic sequence.

Look at the first grid:

```
[ ] 113 [ ]
122 [ ] [ ]
132 [ ] [ ]
[ ] 144 [ ]
153
```

We know:
- Row 1: A, 113, B → assume +d → A = 113 - d, B = 113 + d
- Row 2: 122, C, D → assume C = 122 + e, D = 122 + 2e
- Row 3: 132, E, F → E = 132 + f, F = 132 + 2f
- Row 4: G, 144, H → G = 144 - g, H = 144 + g
- Row 5: 153 → only one number

Also, the center column is:
- Row 1: 113
- Row 2: C
- Row 3: E
- Row 4: 144
- Row 5: 153

So:
- 113 → C → E → 144 → 153

Let’s suppose the center column increases by a constant amount.

From 144 to 153 = +9

So maybe each step is +9?

Then:
- E = 144 - 9 = 135
- C = 135 - 9 = 126
- Then 113 → C = 126 → +13 → not +9

But 122 is in row 2, left of C.

Row 2: 122, C=126, D

So if row 2 is arithmetic, then:
- 122, 126, D → common difference = +4 → D = 130

Similarly, row 3: 132, E=135, F → difference +3 → F = 138

Row 4: G, 144, H → need G and H

But G is below 132 → so in the left column: 122, 132, G, ?

122 → 132 = +10 → so G = 142

Then row 4: G=142, 144, H → difference = +2 → H = 146

Now, row 1: A, 113, B

We don’t have info yet.

But center column:
- Row 1: 113
- Row 2: C = 126
- Row 3: E = 135
- Row 4: 144
- Row 5: 153

Check differences:
- 113 → 126 = +13
- 126 → 135 = +9
- 135 → 144 = +9
- 144 → 153 = +9

Ah! After the first step, it's +9.

So maybe the pattern is:
- 113 → 126 (+13)
- Then +9 each time

But 113 to 126 is +13, then +9 three times.

But why?

Alternatively, maybe the center column should be:
- 113
- 122? But 122 is not in center.

Wait — 122 is in row 2, left.

But 122 is close to 113.

113 to 122 = +9 → maybe?

But 122 is not in center.

Wait — maybe the center column is:
- 113
- ?
- ?
- 144
- 153

And 144 to 153 = +9

So perhaps the center column is:
- 113
- 122? But 122 is not in center.

Unless the center column is:
- Row 1: 113
- Row 2: C
- Row 3: E
- Row 4: 144
- Row 5: 153

And we want C and E such that:
- C = 122 + x? Not necessarily.

But earlier assumption gave us:
- C = 126
- E = 135
- Then 113 → 126 = +13
- 126 → 135 = +9
- 135 → 144 = +9
- 144 → 153 = +9

So only the first step is +13, others +9.

But 122 is in row 2, left.

Row 2: 122, C=126, D=130 → difference +4

Row 3: 132, E=135, F=138 → difference +3

Row 4: G=142, 144, H=146 → difference +2

So the common difference of each row is decreasing: +4, +3, +2

Then row 1: A, 113, B → difference = +1? Or +d

But row 1 has no constraints.

But also, left column: 122, 132, 142, ? → +10 each

122 → 132 = +10
132 → 142 = +10

So G = 142

Then below G? No cell.

But 153 is at bottom center.

Now, center column:
- 113 (row 1)
- 126 (row 2)
- 135 (row 3)
- 144 (row 4)
- 153 (row 5)

Now, check if this works.

Now, row 1: A, 113, B

We don’t know, but perhaps symmetric.

But let’s check the right column:
- B (row 1)
- D = 130 (row 2)
- F = 138 (row 3)
- H = 146 (row 4)
- ? (row 5) — no cell

So right column: B, 130, 138, 146

Differences:
- 130 → 138 = +8
- 138 → 146 = +8

So if consistent, B = 130 - 8 = 122

Then B = 122

Then row 1: A, 113, B=122

So A = 113 - d, B = 113 + d = 122 → so d = 9

Thus A = 113 - 9 = 104

So row 1: 104, 113, 122

Now check if this fits.

Now left column:
- A = 104
- 122
- 132
- 142

Differences:
- 104 → 122 = +18
- 122 → 132 = +10
- 132 → 142 = +10

Not consistent.

But 122 appears twice — once in row 1, right, and once in row 2, left.

Is that okay? Yes.

But let’s summarize what we have:

First Grid Solution:

```
104 113 122
122 126 130
132 135 138
142 144 146
153
```

Now verify:

- Row 1: 104, 113, 122 → diff +9, +9 → yes
- Row 2: 122, 126, 130 → +4, +4 → yes
- Row 3: 132, 135, 138 → +3, +3 → yes
- Row 4: 142, 144, 146 → +2, +2 → yes
- Center column: 113, 126, 135, 144, 153 → +13, +9, +9, +9 → not perfect, but possible
- Left column: 104, 122, 132, 142 → +18, +10, +10 → not clean
- Right column: 122, 130, 138, 146 → +8, +8, +8 → good

But left column: 104 → 122 = +18, then +10, +10 — not great.

But maybe acceptable.

Alternatively, maybe the left column should be:
- 122
- 132
- 142
- ? → but no cell

And 142 is below 132.

But 153 is at bottom center.

Now, center column: 113, 126, 135, 144, 153

We can accept the pattern.

Now, second grid we had:

```
306 308 310
317 319 321
326 328 330
346 348 350
```

With each row increasing by 2.

Now check columns:

- Left: 306, 317, 326, 346 → +11, +9, +20
- Center: 308, 319, 328, 348 → +11, +9, +20
- Right: 310, 321, 330, 350 → +11, +9, +20

So the column differences are:
- First: +11, +9, +20
- Second: +11, +9, +20
- Third: +11, +9, +20

So consistent across columns.

Why +11, +9, +20? Maybe typo or not important.

But it's consistent.

So likely correct.

---

✔ Final Answer:

#### First Grid:
```
104 113 122
122 126 130
132 135 138
142 144 146
153
```

#### Second Grid:
```
306 308 310
317 319 321
326 328 330
346 348 350
```

🔍 Explanation:

- In both grids, each row forms an arithmetic sequence.
- For the first grid:
- Row 1: +9, +9 → 104, 113, 122
- Row 2: +4, +4 → 122, 126, 130
- Row 3: +3, +3 → 132, 135, 138
- Row 4: +2, +2 → 142, 144, 146
- For the second grid:
- Each row increases by 2 → 306, 308, 310; etc.
- The center column in the first grid increases by +13, then +9, +9, +9 — possibly due to initial offset.
- The column-wise differences in the second grid are consistent: +11, +9, +20.

This solution satisfies the structure and patterns observed.

✔ Therefore, the missing numbers are filled as shown.