Number Fill In Puzzle 7: Solve the grid by placing the correct numbers from the provided list into the empty spaces.

To solve this Number Fill In Puzzle, we need to fit the numbers from the list into the grid. The green squares are blocked off, and the white squares are where the numbers go. Numbers can go across (horizontally) or down (vertically).

Here is the step-by-step logical deduction to find where each number belongs:

Step 1: Start with the given clues.
* There is a 4 already filled in at Row 1, Column 6.
* There is a sequence 4 8 7 at the bottom right (Row 13, Columns 12-14). This corresponds to the 3-digit number 487.

Step 2: Analyze the vertical column in the middle (Column 6).
* Looking down Column 6, we see single digits separated by blocks: 4, 9, 2, 6, 3, 9, 1.
* Let's look at the vertical spaces connected to these digits.
* Below the 1 (Row 8, Col 6), there is a vertical space of 5 boxes (Rows 9-13).
* Above the 4 (Row 1, Col 6), there is no space.
* Between 4 and 9 (Row 2, Col 6) is just one box? No, Row 2 Col 6 is the '9'. The space is between Row 1 and Row 2? No, they are adjacent.
* Let's look at the vertical run starting at Row 9, Col 6. It goes down to Row 13. That is 5 digits.
* Let's look at the vertical run starting at Row 1, Col 6. It goes down to Row 8? No, there are blocks.
* Actually, let's look at the vertical strip in Column 6 from Row 1 to Row 8. The cells are:
R1: 4
R2: 9
R3: 2
R4: 6
R5: 3
R6: 9
R7: (Block) - Wait, Row 7 Col 6 is empty/white? Let's check the image carefully.
Row 7 Col 6 is white. Row 8 Col 6 is '1'.
So we have a vertical sequence: 4, 9, 2, 6, 3, 9, [space], 1.
This doesn't form a single word. These are likely intersections with horizontal words.

Let's look for unique lengths first.

Step 3: Identify 7-Digit Numbers.
The 7-digit numbers are: `3410756`, `4926391`, `5196324`, `6245129`, `8643029`, `9527683`.

* Look at Row 2. It has a long horizontal white space from Col 2 to Col 8?
* Row 2: Block, White, Block, White, White, 9, White, White, White, White, White, White, White.
* Actually, let's trace Row 2 carefully.
* Col 1: Block. Col 2: White. Col 3: Block. Col 4: White. Col 5: White. Col 6: 9. Col 7: White. Col 8: White. Col 9: White. Col 10: White. Col 11: White. Col 12: White. Col 13: White.
* This row is fragmented.

Let's look at Column 1.
* Rows 2-3 are blocks? No.
* Let's look at Column 13 (second from right).
* Row 1: Block.
* Row 2-3: White? No, Row 2 Col 13 is white. Row 3 Col 13 is block.
* This is tricky without a coordinate system. Let's look for obvious long lines.

Horizontal Long Lines:
* Row 2: From Col 7 to Col 13?
* Col 6 is 9. Col 7-13 are white. That's 7 digits.
* Does a 7-digit number start after a 9? Or is the 9 part of it?
* If the 9 is part of it, it would be an 8-digit slot, but we only have up to 7 digits. So the 9 is likely a vertical intersection.
* So, Row 2, Cols 7-13 is a 7-digit number.
* Candidates: `3410756`, `4926391`, `5196324`, `6245129`, `8643029`, `9527683`.

* Row 13: We have `4 8 7` at Cols 12-14.
* To the left, Cols 8-11 are white?
* Row 13: Col 1-4 Blocks? Col 5 White. Col 6 Block. Col 7 White?
* Let's re-examine Row 13.
* Cols 1-4: Green/Green/Green/Green? No, Col 1-4 are Green.
* Col 5: White.
* Col 6: Green.
* Col 7: White? No, looking at the grid, Row 13 Col 7 is White.
* Col 8-11: White.
* Col 12-14: 4, 8, 7.
* So we have a 5-digit space at Cols 7-11? Or does it connect to 487?
* Col 11 is next to Col 12 (4). So Cols 7-11 is 5 digits. Then 487 is separate.
* Wait, is Col 6 Green? Yes. Is Col 7 White? Yes.
* So Row 13 has a 5-digit slot at Cols 7-11 and a 3-digit slot at Cols 12-14 (`487`).

Vertical Long Lines:
* Column 6:
* We established digits 4,9,2,6,3,9,1.
* Let's look at Column 5.
* Row 1: White. Row 2: White. Row 3: White. Row 4: White. Row 5: White. Row 6: White. Row 7: White. Row 8: White.
* It looks like Column 5 has a long vertical run from Row 1 to Row 8?
* Let's check blocks in Col 5.
* R1: White. R2: White. R3: White. R4: White. R5: White. R6: White. R7: White. R8: White.
* R9: Block? Row 9 Col 5 is Green.
* So Col 5, Rows 1-8 is an 8-digit space? But we only have up to 7-digit numbers.
* Ah, Row 1 Col 5 is White. Row 2 Col 5 is White. ... Row 8 Col 5 is White.
* Wait, Row 1 Col 6 is 4. Row 2 Col 6 is 9.
* Maybe the vertical number is in Col 4? Or Col 7?

Let's try a different anchor. The number 4926391.
This is a 7-digit number. Notice the digits: 4, 9, 2, 6, 3, 9, 1.
Look at Column 6 again.
Row 1: 4
Row 2: 9
Row 3: 2
Row 4: 6
Row 5: 3
Row 6: 9
Row 7: ?
Row 8: 1
If Row 7 Col 6 is white, then Column 6, Rows 1-8 contains the sequence 4,9,2,6,3,9,[digit],1.
If the number is 4926391, it fits perfectly in Rows 1-7?
Row 1: 4
Row 2: 9
Row 3: 2
Row 4: 6
Row 5: 3
Row 6: 9
Row 7: 1
But Row 8 is also 1. And Row 7 Col 6 is white in the image?
Let's check Row 7 Col 6. In the image, Row 7 Col 6 is WHITE.
Row 8 Col 6 is '1' (pre-filled? No, the pre-filled is Row 8 Col 6 = 1? The prompt says "One of the numbers has been done for you." The image shows a '1' at R8C6 and '4' at R1C6 and '487' at R13).
Actually, looking closely at the provided solution logic for these types of puzzles:
The vertical column 6 has the digits:
R1: 4
R2: 9
R3: 2
R4: 6
R5: 3
R6: 9
R7: (Empty)
R8: 1
If we place 4926391 vertically in Column 6, Rows 1-7:
R1: 4 (Matches)
R2: 9 (Matches)
R3: 2 (Matches)
R4: 6 (Matches)
R5: 3 (Matches)
R6: 9 (Matches)
R7: 1
Then R8 is '1'. This would mean two 1s touching? Or is R8 part of another word?
If R7C6 is 1, then the vertical word is done. The '1' at R8C6 might be the start of a new vertical word or part of a horizontal one.
However, usually, these puzzles don't have overlapping numbers like that unless specified.
Let's assume 4926391 goes in Column 6, Rows 1-7.
This fills:
R1C6=4, R2C6=9, R3C6=2, R4C6=6, R5C6=3, R6C6=9, R7C6=1.

Now, what about the '1' at R8C6?
It is likely the last digit of a vertical number ending there, or the first digit of one starting there.
Since R7C6 is now 1, and R8C6 is 1, they are adjacent.
Let's look at horizontal words intersecting this column.

Intersections with Column 6 (Vertical 4926391):

1. Row 1: ` _ _ _ _ 4 _ _ _ _ _ _ _ _ `
* C6 is 4.
* Left: C1-C5. C1-C4 are White? C5 is White.
* Right: C7-C13. C7-C13 are White?
* Let's check Row 1 blocks.
* C1-C4: White. C5: White. C6: 4. C7: Green? No, C7 is White in Row 1?
* Looking at Row 1: C1-C5 White. C6=4. C7 Green. C8-C10 White? C11 Green? C12-C13 Green?
* Actually, let's look at the top right. R1 C7 is Green. R1 C8-C10 White. R1 C11 Green. R1 C12-C13 Green.
* So Row 1 Right side is C8-C10 (3 digits).
* Row 1 Left side is C1-C5 (5 digits).

2. Row 2: ` _ _ _ _ _ 9 _ _ _ _ _ _ _ `
* C6 is 9.
* Left: C1 Green. C2 White. C3 Green. C4 White. C5 White.
* So Left is C4-C5 (2 digits)? Or C2 (1 digit)?
* Right: C7-C13 White. That's 7 digits.
* We have a 7-digit horizontal slot at Row 2, Cols 7-13.
* It intersects Col 6 (which is outside this slot).
* So we need a 7-digit number for R2C7-13.

3. Row 3: ` _ _ _ _ _ 2 _ _ _ _ _ _ _ `
* C6 is 2.
* Left: C1-C3 White? C4 Green? C5 White?
* Right: C7 Green? C8-C9 White? C10 Green? C11-C13 White?

Let's refine the Grid Structure based on visual inspection:

Row 1:
* C1-C5: White (5 spaces). -> Needs a 5-digit number.
* C6: 4 (from Vert 4926391).
* C7: Green.
* C8-C10: White (3 spaces). -> Needs a 3-digit number.
* C11-C13: Green.

Row 2:
* C1: Green.
* C2: White (1 space). -> Needs a 1-digit? No, min is 3. Must be part of vertical.
* C3: Green.
* C4-C5: White (2 spaces). -> Part of vertical?
* C6: 9 (from Vert 4926391).
* C7-C13: White (7 spaces). -> Needs a 7-digit number.

Row 3:
* C1-C3: White (3 spaces). -> Needs a 3-digit number.
* C4: Green.
* C5: White (1 space). -> Vertical.
* C6: 2 (from Vert 4926391).
* C7: Green.
* C8-C9: White (2 spaces). -> Vertical?
* C10: Green.
* C11-C13: White (3 spaces). -> Needs a 3-digit number.

Row 4:
* C1: Green.
* C2-C4: White (3 spaces). -> Needs a 3-digit number.
* C5: Green.
* C6: 6 (from Vert 4926391).
* C7-C8: White (2 spaces). -> Vertical?
* C9-C13: White? Let's check.
* R4 C7 White, C8 White. C9 Green? C10-C13 White?
* Actually, let's look at the block pattern.
* R4: G, W, W, W, G, 6, W, W, G, W, W, W, W?
* Let's assume standard puzzle density.

Let's use the numbers to constrain the slots.

Slot Analysis:

A. 7-Digit Slots:
1. Row 2, Cols 7-13.
2. Are there others?
* Col 1? R2-R8?
* Row 13? No.
* Let's check Column 1.
* R1: W. R2: G. R3: W. R4: G. R5: G. R6: W. R7: W. R8: G. R9: G. R10: G. R11: W. R12: W. R13: G.
* Not long enough.
* Let's check Column 13.
* R1: G. R2: W. R3: W. R4: W. R5: W. R6: W. R7: W. R8: W. R9: W. R10: G. R11: G. R12: W. R13: 7.
* R2-R9 is 8 digits. Too long? Or maybe R10 is not Green?
* If R2-R9 is 8 digits, we don't have 8-digit numbers.
* Maybe it splits?

Let's look at the 7-digit candidates again:
`3410756`, `4926391` (Used in Col 6), `5196324`, `6245129`, `8643029`, `9527683`.

We used `4926391` in Col 6.
Remaining 7-digit numbers: `3410756`, `5196324`, `6245129`, `8643029`, `9527683`.

Slot: Row 2, Cols 7-13.
This slot intersects with vertical columns 7 through 13.
Let's determine the first digit of this number.
It is at R2C7.
Is there a vertical number passing through R2C7?
Col 7:
R1: G.
R2: W (Start of 7-digit horiz).
R3: G.
So R2C7 is the TOP of a vertical word? No, R1 is Green. So R2C7 is the START of a vertical word going DOWN?
Let's check Col 7 downwards.
R2: W.
R3: G.
So Col 7 at Row 2 is a 1-digit vertical? Impossible.
Therefore, the cell R2C7 is ONLY part of the horizontal 7-digit number. It does not intersect a vertical number (except potentially at the ends if the vertical starts/ends there, but R3 is Green, so no vertical continues down).
Wait, if R3C7 is Green, then the vertical space at Col 7 is just Row 2? That's length 1. No numbers have length 1.
This implies my grid reading is slightly off or the number intersects elsewhere.
Let's re-read Row 3 Col 7.
Row 3: `W W W G W 2 G W W G W W W`
If R3C7 is Green, then yes, Col 7 has no vertical neighbor at R3.
What about R1C7? Green.
So R2C7 is isolated vertically? That can't be right for a fill-in puzzle unless it's a very short vertical, but we don't have 1-digit numbers.
Perhaps R3C7 is NOT Green?
Looking at the image:
Row 3: Cells 1,2,3 are White. Cell 4 is Green. Cell 5 is White. Cell 6 is 2. Cell 7 is GREEN. Cell 8,9 White. Cell 10 Green. Cell 11,12,13 White.
Okay, so R3C7 is definitely Green.
And R1C7 is Green.
So Col 7, Row 2 is a single white cell surrounded by greens vertically.
This means the digit at R2C7 is part of the horizontal number, but DOES NOT form a vertical number.
This is allowed. Not every cell needs to be part of both a horizontal and vertical word.

So, we just need to fit a 7-digit number in R2C7-13.
How do we choose which one?
We need to look at the intersections with other rows/cols that DO have vertical words.

Let's look at Row 13.
We identified `487` at C12-14.
Left of it, C7-11 is a 5-digit horizontal slot.
Candidates for 5 digits: `34107`, `81526`, `47023`, `84272`, `49132`, `92053`, `69173`.

Let's look at Column 12.
R1: G.
R2: W (Part of 7-digit Horiz R2).
R3: W (Part of 3-digit Horiz R3 C11-13).
R4: W.
R5: W.
R6: W.
R7: W.
R8: W.
R9: G?
R10: G?
R11: G?
R12: W.
R13: 8 (from 487).

Let's trace Col 12 carefully.
R2C12 is the 6th digit of the 7-digit number in Row 2.
R3C12 is the 2nd digit of the 3-digit number in Row 3 (C11-13).
R4C12...
Let's look at the block at R9/R10/R11.
In the image, Rows 9-11 seem to have blocks in the middle right.
R9: C10-C12 Green?
R10: C10-C12 Green?
R11: C10-C12 Green?
If so, Col 12 is split.
Top part: R2-R8 (7 digits).
Bottom part: R12-R13?
R12C12 is White. R13C12 is 4.
So R12-R13 is 2 digits? No 2-digit numbers.
Maybe R11C12 is White?
Let's look at the cluster at Bottom Right.
R12: `W W W W W W W W W W W W W`? No.
R12: C1-C4 G? C5 W? C6 G? C7-C10 W? C11 G? C12 W? C13 W? C14 G?
This is getting too speculative. Let's look for a stronger constraint.

Strong Constraint: The number 4926391 is Vertical Col 6.
Digits:
R1C6: 4
R2C6: 9
R3C6: 2
R4C6: 6
R5C6: 3
R6C6: 9
R7C6: 1

Now look at Row 7.
R7C6 is 1.
Row 7 structure:
C1-C4: White?
C5: White?
C6: 1.
C7-C8: White?
C9: Green?
C10-C11: White?
C12-C13: White?

Let's look at Row 6.
R6C6 is 9.
Row 6 structure:
C1-C4: White?
C5: White?
C6: 9.
C7-C8: White?
C9: Green?
C10-C11: White?
C12-C13: White?

Let's try to place the 3-digit number 487 at R13 C12-14.
This fixes:
R13C12 = 4
R13C13 = 8
R13C14 = 7

Now look at Column 13.
R13C13 = 8.
Above it, R12C13 is White.
R11C13 is Green?
If R11C13 is Green, then Col 13 has a vertical slot at R12-R13 (2 digits). No.
Maybe R10-R13?
Let's assume there is a vertical number ending in 8 at R13C13.
Or starting with 8?
If it's a 3-digit number ending in 8: `_ _ 8`.
If it's a 4-digit number ending in 8: `_ _ _ 8`.

Let's look at the 3-digit numbers:
`228`, `375`, `487` (Used), `735`, `947`, `963`.

Does any 3-digit number end in 8? 228.
If 228 is in Col 13, Rows 11-13?
R11C13=2, R12C13=2, R13C13=8.
This requires R11C13 to be White.
Let's check the image for R11C13.
Row 11: `G G W G G G G G G G G W G`?
Actually, Row 11 looks like:
C1-C2 Green.
C3 White.
C4-C12 Green?
C13 White?
C14 Green?
If C13 is White, and C12 is Green, and C14 is Green...
Then Col 13 at Row 11 is isolated horizontally?
If R11C13 is part of a vertical word, and R12C13 is part of it, and R13C13 is 8.
If the word is 228, then R11C13=2, R12C13=2.

Let's test this hypothesis: Col 13, Rows 11-13 is 228.
This puts `2` at R11C13 and `2` at R12C13.

Now, what is at Row 12?
R12C13 is 2.
Row 12 has a long horizontal stretch?
R12: C5 White, C7-C11 White, C12 White, C13 2.
Let's look at Row 12, Cols 7-12.
That's 6 digits.
Do we have a 6-digit number ending in 2?
6-digit candidates: `130453`, `307518`, `340289`, `425934`, `647538`, `682984`, `815397`.
None end in 2.
So R12C7-12 is probably not a single 6-digit number ending at C12.
Maybe the number is shorter?
Or maybe Col 13 is not 228.

Let's look at 375. Ends in 5.
735. Ends in 5.
947. Ends in 7.
963. Ends in 3.

What if Col 12 has a number?
R13C12 is 4.
If a 3-digit number ends in 4? None.
If a 3-digit number starts with 4? `487` is used.
Is there another 4xx? No.

Let's look at Row 13, Cols 7-11 (5 digits).
Let's call this H13_5.
It intersects Col 7, 8, 9, 10, 11.

Let's look at Col 11.
R13C11 is the last digit of H13_5.
R12C11 is White.
R11C11 is Green?
If R11C11 is Green, then Col 11 has a slot R12-R13 (2 digits). No.
So R11C11 must be White?
If R11C11 is White, let's look at Row 11.
Row 11 seems to have very few white squares.
Actually, looking at the bottom left:
Row 12: C2 Green, C3-C5 White?
Row 13: C1-C4 Green, C5 White, C6 Green...

Let's try a different entry point. The number 3410756.
Where can a 7-digit number go?
Only Row 2 C7-13 seems to be the main 7-digit horizontal slot.
Let's assume Row 2 C7-13 is 3410756.
Digits:
R2C7=3
R2C8=4
R2C9=1
R2C10=0
R2C11=7
R2C12=5
R2C13=6

Now check intersections.
Col 7: R2C7=3.
R1C7 is Green.
R3C7 is Green.
So Col 7 at R2 is isolated vertically. OK.

Col 8: R2C8=4.
R1C8 is White (Part of R1 C8-10 3-digit slot).
R3C8 is White (Part of R3 C8-9 2-digit? Or vertical?).
Let's look at Col 8.
R1C8: Top of a vertical?
R2C8: 4.
R3C8: White.
R4C8: White.
R5C8: White?
R6C8: White?
R7C8: White?
R8C8: White?
R9C8: Green?
If Col 8 has a vertical run from R1 to R8, that's 8 digits. Too long.
Maybe it breaks?
R1C8-C10 is a 3-digit horizontal.
Let's say R1 C8-10 is a 3-digit number.
It intersects Col 8, 9, 10 at Row 1.

Col 9: R2C9=1.
R1C9 is Middle of R1 C8-10.
R3C9 is White.

Col 10: R2C10=0.
R1C10 is End of R1 C8-10.
R3C10 is Green.
So Col 10 at R2 is 0.
R1C10 is part of the 3-digit number.
R3C10 is Green.
So Col 10 has a vertical slot R1-R2? Length 2. No.
So R1C10 and R2C10 do not form a vertical number together?
Or maybe R1C10 is the END of a vertical number coming from above? No, R1 is top.
So R1C10 must be part of a vertical number going DOWN?
But R3C10 is Green. So the vertical number would be R1-R2 (2 digits). Impossible.
Therefore, R2C10 cannot be 0 if it creates an invalid vertical fragment?
Unless R1C10 is NOT part of a vertical number, and R2C10 is NOT part of a vertical number.
But R2C10 is 0. Is 0 allowed as a standalone digit? No, it's part of the horizontal 3410756.
Does R2C10 intersect a vertical number?
If R1C10 is White and R3C10 is Green, then Col 10 at R2 is isolated vertically IF R1C10 is also not forming a vertical pair.
Wait, if R1C10 is White, it MUST be part of a number.
Horizontal: R1 C8-10 (3 digits).
Vertical: If R2C10 is White, and R1C10 is White, and R3C10 is Green, then R1-R2 is a 2-digit vertical slot.
We don't have 2-digit numbers.
So, R2C10 cannot be White if R1C10 is White and R3C10 is Green.
BUT R2C10 IS White in the grid (part of the 7-digit slot).
And R1C10 IS White in the grid.
And R3C10 IS Green in the grid.
This creates a 2-digit vertical slot at Col 10, Rows 1-2.
Since there are no 2-digit numbers, this configuration is IMPOSSIBLE with the number `3410756` (or any number) in Row 2 C7-13 UNLESS one of the cells is actually Green.
Let's re-examine the image for R3C10.
Row 3: `W W W G W 2 G W W G W W W`
C10 is Green. Correct.
Row 1: `W W W W W 4 G W W G G G G`?
Let's check R1C10.
R1 C8, C9, C10 are White.
R1 C11 is Green.
So R1 C8-10 is a 3-digit horizontal.
Col 10: R1 White, R2 White, R3 Green.
This forms a 2-digit vertical slot.
Contradiction.

Did I misidentify the 7-digit slot?
Maybe Row 2 C7-13 is NOT the slot.
Maybe the 7-digit number is VERTICAL?
Where is a 7-digit vertical slot?
Col 6 is 4926391.
Col 1? No.
Col 13?
Col 12?
Col 5?
Col 4?

Let's look at Column 1.
R1 W, R2 G, R3 W, R4 G, R5 G, R6 W, R7 W, R8 G, R9 G, R10 G, R11 W, R12 W, R13 G.
No.

Let's look at Column 2.
R1 W, R2 W, R3 W, R4 W, R5 W, R6 W, R7 W, R8 W, R9 W, R10 W, R11 G, R12 G, R13 G?
If Col 2 is White from R1 to R10, that's 10 digits. Too long.

Let's look at Column 3.
R1 W, R2 G, R3 W, R4 W, R5 W, R6 W, R7 W, R8 W, R9 W, R10 W, R11 W, R12 W, R13 G?
Long.

Maybe the 7-digit number is Row 13?
No, we have 487.

Maybe the 7-digit number is Row 1?
No, fragmented.

Let's reconsider the 2-digit vertical slot at Col 10, R1-2.
Is it possible that R1C10 is GREEN?
Looking at the image:
Row 1: C6=4. C7=Green. C8=White. C9=White. C10=White. C11=Green.
It really looks like 3 whites.

Is it possible that R3C10 is WHITE?
Row 3: C6=2. C7=Green. C8=White. C9=White. C10=Green.
It really looks like Green.

Is it possible that R2C10 is GREEN?
Row 2: C6=9. C7-C13 White.
It really looks like White.

There is a contradiction in my grid reading or the puzzle design.
Wait! Look at Row 2 C11.
If the 7-digit number is `3410756`, R2C11=7.
Col 11:
R1C11 is Green.
R2C11 is 7.
R3C11 is White.
R4C11 is White?
If R1 is Green, R2 is White, R3 is White...
Then Col 11 has a vertical slot starting at R2.
If it goes down to R8?
R2-R8 is 7 digits.
Do we have a 7-digit vertical number in Col 11?
Candidates: `5196324`, `6245129`, `8643029`, `9527683`.

If Col 11, Rows 2-8 is a 7-digit number:
R2C11 is the first digit.
From `3410756` in Row 2, R2C11 is the 5th digit = 7.
So the vertical number in Col 11 must start with 7.
None of the remaining 7-digit numbers start with 7.
(`519...`, `624...`, `864...`, `952...`).
So `3410756` is likely WRONG for Row 2.

Let's try another 7-digit number for Row 2 C7-13.
Must result in a valid vertical intersection at Col 11 (and others).
Col 11 Vertical Slot: R2-R8 (7 digits). Starts with R2C11.
Col 12 Vertical Slot: R2-R8?
R1C12 Green. R2C12 White. R3C12 White...
If Col 12 is also R2-R8 (7 digits).
Col 13 Vertical Slot: R2-R8?
R1C13 Green. R2C13 White...

So we have THREE vertical 7-digit slots in Cols 11, 12, 13, all starting at Row 2.
And one horizontal 7-digit slot in Row 2, Cols 7-13.

The horizontal number provides the FIRST DIGIT for the vertical numbers in Cols 11, 12, 13.
Let H be the horizontal number.
H = d1 d2 d3 d4 d5 d6 d7
Cols 7, 8, 9, 10, 11, 12, 13.
So:
Col 11 starts with d5.
Col 12 starts with d6.
Col 13 starts with d7.

We need 3 vertical 7-digit numbers starting with d5, d6, d7.
Available 7-digit numbers (excluding 4926391):
`3410756` (Starts 3)
`5196324` (Starts 5)
`6245129` (Starts 6)
`8643029` (Starts 8)
`9527683` (Starts 9)

So d5, d6, d7 must be chosen from {3, 5, 6, 8, 9}.

Let's check the horizontal candidates for H:
1. `3410756`: d5=7, d6=5, d7=6.
Need verticals starting with 7, 5, 6.
We have 5 (`5196324`) and 6 (`6245129`).
Do we have a 7? NO.
So `3410756` is out.

2. `5196324`: d5=3, d6=2, d7=4.
Need verticals starting with 3, 2, 4.
We have 3 (`3410756`).
Do we have 2? NO.
Do we have 4? NO (4926391 is used in Col 6).
So `5196324` is out.

3. `6245129`: d5=1, d6=2, d7=9.
Need verticals starting with 1, 2, 9.
Do we have 1? NO.
Do we have 2? NO.
Do we have 9? YES (`9527683`).
So `6245129` is out.

4. `8643029`: d5=0, d6=2, d7=9.
Need verticals starting with 0, 2, 9.
Do we have 0? NO.
So `8643029` is out.

5. `9527683`: d5=6, d6=8, d7=3.
Need verticals starting with 6, 8, 3.
We have 6 (`6245129`).
We have 8 (`8643029`).
We have 3 (`3410756`).
MATCH!

So:
Horizontal Row 2 C7-13 is `9527683`.
This sets:
R2C7=9
R2C8=5
R2C9=2
R2C10=7
R2C11=6
R2C12=8
R2C13=3

And the Vertical Numbers are:
Col 11, Rows 2-8 starts with 6: Must be `6245129`.
Col 12, Rows 2-8 starts with 8: Must be `8643029`.
Col 13, Rows 2-8 starts with 3: Must be `3410756`.

Let's verify the digits in the grid:
Col 11 (6245129):
R2C11=6 (Matches H)
R3C11=2
R4C11=4
R5C11=5
R6C11=1
R7C11=2
R8C11=9

Col 12 (8643029):
R2C12=8 (Matches H)
R3C12=6
R4C12=4
R5C12=3
R6C12=0
R7C12=2
R8C12=9

**Col