首先，用户提供了一个6x6数独的题目，我需要解出这个数独。数独的规则是：在一个6x6的网格中，每行、每列都必须包含数字1到6，且不重复。网格被划分为两个3x2的子网格，每个子网格也必须是1到6的数字各出现一次。

题目给出的网格是：

行1: 2, X, X, |, X, 4, X

行2: 1, X, 4, |, 6, X, X

行3: ------------ (分隔线)

行4: 6, X, 1, |, X, X, X

行5: 4, 2, X, |, 3, X, 1

行6: ------------ (分隔线)

行7: X, X, X, |, 2, X, X

行8: 3, 4, X, |, X, X, X

网格是用竖线和分隔线表示的，但为了清晰，我应该将其转化为一个6x6的矩阵。

让我列出网格的行和列：

• 行1: 位置 (1,1)=2, (1,2)=X, (1,3)=X, (1,4)=X, (1,5)=4, (1,6)=X

竖线分隔子网格：| 表示在列3和列4之间分割，所以子网格1是列1-3，子网格2是列4-6？等等，不对。

题目说：“在一个3x2的网格中”，并且“网格一排有2个，一共3排”。意思是整个6x6网格被分成3行，每行有两个3x2的子网格。

但看分隔线，它是在行3和行6之间有分隔线，但行是：

用户输入是：

"2 X X | X 4 X"

"1 X 4 | 6 X X"

"-------------" 这应该是行分隔

"6 X 1 | X X X"

"4 2 X | 3 X 1"

"-------------" 另一个分隔

"X X X | 2 X X"

"3 4 X | X X X"

所以，实际上，有6行数据：

行1: 2, X, X, |, X, 4, X

行2: 1, X, 4, |, 6, X, X

然后分隔线

行3: 6, X, 1, |, X, X, X

行4: 4, 2, X, |, 3, X, 1

然后另一个分隔线

行5: X, X, X, |, 2, X, X

行6: 3, 4, X, |, X, X, X

竖线|在每行的第4个位置，意思是列被分成两部分：列1-3和列4-6。

每个部分是一个3x2子网格？不，整个是6x6，所以每行有6列。

列索引：让列从左到右为1到6。

在每行中，| 出现在第4个元素前，意思是：

例如行1: 元素1:2, 元素2:X, 元素3:X, |, 元素4:X, 元素5:4, 元素6:X

所以，实际上，列1,2,3是第一个子网格（左），列4,5,6是第二个子网格（右）。

同样，行被分成两个块：行1-2是上部的两个子网格，行3-4是中间，行5-6是下部？但分隔线是水平分隔在行2和行3之间？用户输入有"------------"在行2和行3之间，以及在行4和行5之间。

用户输入：

"2 X X | X 4 X" // 行1

"1 X 4 | 6 X X" // 行2

"-------------" // 分隔线，意思是新行开始

"6 X 1 | X X X" // 行3

"4 2 X | 3 X 1" // 行4

"-------------" // 另一个分隔

"X X X | 2 X X" // 行5

"3 4 X | X X X" // 行6

所以，有6行数据：

• 行1: 列1=2, 列2=X, 列3=X, 列4=X, 列5=4, 列6=X

• 行2: 列1=1, 列2=X, 列3=4, 列4=6, 列5=X, 列6=X

• 行3: 列1=6, 列2=X, 列3=1, 列4=X, 列5=X, 列6=X

• 行4: 列1=4, 列2=2, 列3=X, 列4=3, 列5=X, 列6=1

• 行5: 列1=X, 列2=X, 列3=X, 列4=2, 列5=X, 列6=X

• 行6: 列1=3, 列2=4, 列3=X, 列4=X, 列5=X, 列6=X

竖线|只是视觉分隔，不影响逻辑，但我们需要考虑3x2子网格。

题目说：“填入1-6共6个数字，这样的网格一排有2个，一共3排。” 意思是整个6x6被分成3行子网格，每行有两个3x2的子网格。

每个3x2子网格必须是1-6各一次。

所以，子网格定义：

• 左上：行1-3, 列1-3

• 右上：行1-3, 列4-6

• 左中：行3-5? 等等，行索引。

行：1,2,3为顶部子网格行。

但行1-3覆盖了上部的两个子网格。

类似地，行4-6是下部，但行4和5是？等等。

标准6x6数独划分：通常，6x6数独被分成6个2x3或3x2子网格。

题目指定是3x2网格，一排有2个，所以：

• 顶部一排：两个子网格：左(行1-3,列1-3) 和 右(行1-3,列4-6)

• 中间一排：左(行3-5,列1-3)? 但行3被共享？不，在标准中，子网格是连续的。

看分隔线：水平分隔在行2之后和行4之后，意思是行1-2是顶部，行3-4是中间？但行3和4。

用户输入有分隔在行2和行3之间，以及行4和行5之间。

所以，子网格行：

• 第一排子网格：行1-2？但每个子网格是3行高？题目说“3x2网格”，3行2列。

但这里行只有6行，所以每个子网格块应该是3行高。

但用户的分隔在行2之后和行4之后，意思是：

• 顶部：行1-2？但行1-2只有2行，但应该是3行。

不一致。

或许分隔线表示子网格的边界。

题目说：“这样的网格一排有2个，一共3排。” 所以3排子网格，每排有两个子网格。

每排子网格是3行高。

所以：

• 排1: 行1-3, 有两个子网格： (1-3,1-3) 和 (1-3,4-6)

• 排2: 行4-6, 有两个子网格： (4-6,1-3) 和 (4-6,4-6)

但用户输入中，分隔线在行2和行3之间，以及行4和行5之间，这不对应。

行3和行4在中间。

或许是错误的理解。

在用户输入中，水平分隔线在第二行数据和第三行数据之间，以及在第四行数据和第五行数据之间。

数据行是：

行1, 行2, 然后分隔, 行3, 行4, 然后分隔, 行5, 行6.

所以，行1-2是顶部，行3-4是中间，行5-6是底部？但每个应该是3行高？只有2行。

困惑。

或许“3x2”指的是每个小网格的大小，但整体划分。

另一个想法：或许“3x2网格”意思是子网格是3行2列，但整个6x6有2行这样的子网格排？不，题目说“一共3排”，所以3排。

每排3行高，所以行1-3为第一排，行4-6为第二排？但行是6行，只有2排？但题目说3排。

矛盾。

用户信息: "6x6数独的规则是：在一个3x2的网格中，填入1-6共6个数字，这样的网格一排有2个，一共3排。"

解析： "在一个3x2的网格中" – 可能指的是每个子网格是3行2列，但“网格一排有2个”意思是每行有2个子网格，“一共3排”意思是3行子网格。

但6行高，3排子网格，每排3行，所以行1-3是第一排子网格，行4-6是第二排？但3排需要9行，但只有6行，所以不可能。

或许“3x2”是误述。 标准6x6数独通常是2x3子网格或3x2，但6x6总行6行，所以子网格排数：如果子网格是2行高，则3排子网格排；如果3行高，则2排。

但题目说“3x2网格”和“一共3排”，所以可能子网格是2行高、3列宽？但题目说“3x2”，3行2列。

我困惑了。

看实际网格。

从输入，有6行数据，竖线分隔列3和4，所以列1-3和4-6是子网格区域。

但行：水平分隔在行2之后和行4之后，所以可能行1-2是顶部，行3-4是中间，行5-6是底部，每个部分有2行，但每个子网格应该是3行高？不匹配。

或许在上下文中，“3x2”指的是每个子网格的大小为3行和2列，但整体6x6有2行这样的子网格排（因为6/3=2），但题目说“3排”，所以矛盾。

或许是打字错误或误解。

另一个想法：或许“网格一排有2个”意思是每行有2个子网格，“一共3排”意思是3行，但每个子网格是2行高或3行。

我们忽略“3排”部分，专注于输入。

在输入中，有水平线在行2和行3之间，以及行4和行5之间，所以可能子网格边界在行3和行4之间？但行3是共享的。

标准方式：在6x6数独中，子网格划分是固定的。

从输入，我可以推断子网格：

• 对于行1-2和列1-3：但只有2行，所以不完整。

或许水平线表示子网格的边界，所以：

• 顶部子网格排：行1-2？但只有2行。

我需要假设子网格大小。

从上下文，既然有分隔，可能行1-2是上部的子网格部分，但每个子网格是3行，所以行1-3应该是一个块，但分隔线在行2之后，意思是行1-2是第一个子网格行，但只有2行。

我认为最好的方式是忽略水平分隔线对于行数的含义，而专注于列分隔。

对于列，| 在列4前，所以列1-3和列4-6是两组。

对于行，既然有6行，并且题目说“3排”，但只有2个完整3行块？不。

用户信息: "共同组成一个6x6的大网格。" 所以是6x6网格。

或许“3x2”意思是每个小区域是3x2，但整体有6x6/ (3x2) = 2个这样的区域？但题目说“网格一排有2个”，所以每行有2个子网格。

我放弃了，让我们直接看网格和数字。

数独规则：每行、每列、每个3x2子网格必须包含1-6各一次。

从输入，列分隔：列1-3是左部，列4-6是右部。

行分隔：水平线在行2之后和行4之后，所以可能：

• 上部: 行1-2 for both left and right? but each should be 3 rows.

Perhaps the horizontal lines indicate the boundaries between the row blocks.

For example, after row 2, there is a line, so row 1-2 is one block, then row 3-4 is another, row 5-6 is another, but each block has 2 rows, not 3.

But for a 3x2 subgrid, it should be 3 rows and 2 columns, but here the row blocks are only 2 rows.

Inconsistency.

Perhaps for this puzzle, the subgrids are 2x3 instead of 3x2.

Let's check the rule: "在一个3x2的网格中" – "in a 3x2 grid", but "网格" might refer to the subgrid size.

But "3x2" could be rows x columns or columns x rows.

In some contexts, it might be specified as 3 rows and 2 columns.

But with 6 rows, if subgrids are 3 rows high, then there are 2 rows of subgrids (row 1-3 and row 4-6).

But the puzzle has 3 horizontal divisions in the input with lines after row 2 and after row 4, suggesting that there are three row groups: rows 1-2, rows 3-4, rows 5-6, each of 2 rows.

And for columns, grouped as 1-3 and 4-6.

So each subgrid would be 2x3, not 3x2.

That makes sense because 2 rows high, 3 columns wide.

Then "3x2" might be a misnomer, or perhaps it's written as 3x2 but meaning 3 columns and 2 rows.

In the text: "3x2的网格" and "一排有2个", so if it's 3 columns and 2 rows, then "3x2" could be columns x rows.

In matrix notation, it's often rows x columns, but in context, it might be different.

To resolve, let's look at the number of cells.

Each subgrid should have 6 cells with 1-6 each once.

If subgrid is 2x3, it has 6 cells, perfect.

Similarly, if 3x2, also 6 cells.

But with the input having divisions after row 2 and row 4, it suggests that the row groups are 2 rows each.

So I think for this puzzle, the subgrids are 2 rows high and 3 columns wide.

So there are 3 rows of subgrids (each 2 rows high), and 2 columns of subgrids (each 3 columns wide).

Thus:

• Top row of subgrids: rows 1-2, with left subgrid columns 1-3, right subgrid columns 4-6
• Middle row of subgrids: rows 3-4, with left subgrid columns 1-3, right subgrid columns 4-6
• Bottom row of subgrids: rows 5-6, with left subgrid columns 1-3, right subgrid columns 4-6

Yes, that matches the input format with horizontal lines after row 2 and after row 4.

Similarly for columns, vertical line after column 3, so left subgrid columns 1-3, right subgrid columns 4-6 for each row group.

So subgrids are:

1. Top-left: rows 1-2, cols 1-3
2. Top-right: rows 1-2, cols 4-6
3. Middle-left: rows 3-4, cols 1-3
4. Middle-right: rows 3-4, cols 4-6
5. Bottom-left: rows 5-6, cols 1-3
6. Bottom-right: rows 5-6, cols 4-6

Each must contain 1-6 exactly once.

Also, rows 1-6 each must have 1-6 once, columns 1-6 each must have 1-6 once.

Now, let's write the grid with known numbers:

Row 1: Col1=2, Col2=X, Col3=X, Col4=X, Col5=4, Col6=X

Row 2: Col1=1, Col2=X, Col3=4, Col4=6, Col5=X, Col6=X

Row 3: Col1=6, Col2=X, Col3=1, Col4=X, Col5=X, Col6=X

Row 4: Col1=4, Col2=2, Col3=X, Col4=3, Col5=X, Col6=1

Row 5: Col1=X, Col2=X, Col3=X, Col4=2, Col5=X, Col6=X

Row 6: Col1=3, Col2=4, Col3=X, Col4=X, Col5=X, Col6=X

X means unknown.

Now, I need to solve this Sudoku.

First, let's list all known numbers per cell.

I'll denote the grid as a 6x6 matrix.

Let me make a table or list possibilities.

Since it's text, I'll reason step by step.

Start with row 1: [2, ?, ?, ?, 4, ?]

Row 2: [1, ?, 4, 6, ?, ?]

Row 3: [6, ?, 1, ?, ?, ?]

Row 4: [4, 2, ?, 3, ?, 1]

Row 5: [?, ?, ?, 2, ?, ?]

Row 6: [3, 4, ?, ?, ?, ?]

Now, look at columns.

Column 1: row1=2, row2=1, row3=6, row4=4, row5=?, row6=3

So known: row1=2, row2=1, row3=6, row4=4, row6=3, row5 unknown.

Missing in col1: 5 and possibly others, but numbers missing: 1,2,3,4,6 are present, so missing 5. Row5 col1 must be 5.

Col1: values: 2,1,6,4,?,3

So present: 1,2,3,4,6 missing 5, so row5 col1 must be 5.

Yes.

So row5 col1 = 5.

Now row5: [5, ?, ?, 2, ?, ?]

Similarly, column 2: row1=?, row2=?, row3=?, row4=2, row5=?, row6=4

Known: row4 col2=2, row6 col2=4, others unknown.

Missing numbers: 1,3,5,6? Not all known, so can't determine yet.

Column 3: row1=?, row2=4, row3=1, row4=?, row5=?, row6=?

Known: row2=4, row3=1, so missing 2,3,5,6.

Not enough.

Now, look at subgrids.

First, top-left subgrid: rows 1-2, cols 1-3

Cells: (1,1)=2, (1,2)=?, (1,3)=?, (2,1)=1, (2,2)=?, (2,3)=4

Must contain 1,2,3,4,5,6.

Present: 1,2,4, so missing 3,5,6.

Now, (1,2), (1,3), (2,2) are unknown.

Also, row1 has (1,2) and (1,3) unknown, row2 has (2,2) unknown.

Similarly, top-right subgrid: rows 1-2, cols 4-6

(1,4)=?, (1,5)=4, (1,6)=?, (2,4)=6, (2,5)=?, (2,6)=?

Present: 4,6, so missing 1,2,3,5.

(1,4), (1,6), (2,5), (2,6) unknown.

Now, middle-left subgrid: rows 3-4, cols 1-3

(3,1)=6, (3,2)=?, (3,3)=1, (4,1)=4, (4,2)=2, (4,3)=?

Present: 6,1,4,2, so missing 3,5.

And (3,2) and (4,3) unknown.

(4,3) is row4 col3, which is X, so unknown.

Now, middle-right subgrid: rows 3-4, cols 4-6

(3,4)=?, (3,5)=?, (3,6)=?, (4,4)=3, (4,5)=?, (4,6)=1

Present: 3,1, so missing 2,4,5,6.

(3,4), (3,5), (3,6), (4,5) unknown.

(4,5) is row4 col5, X.

Bottom-left subgrid: rows 5-6, cols 1-3

(5,1)=5 (we found), (5,2)=?, (5,3)=?, (6,1)=3, (6,2)=4, (6,3)=?

Present: 5,3,4, so missing 1,2,6.

(5,2), (5,3), (6,3) unknown.

Bottom-right subgrid: rows 5-6, cols 4-6

(5,4)=2, (5,5)=?, (5,6)=?, (6,4)=?, (6,5)=?, (6,6)=?

All unknown except (5,4)=2.

Present: 2, so missing 1,3,4,5,6.

Now, back to row1.

Row1: [2, ?, ?, ?, 4, ?]

Missing numbers: 1,3,5,6 (since 2 and 4 present)

But row has 6 cells, so must have 1,3,5,6 in the ? positions.

Similarly, row2: [1, ?, 4, 6, ?, ?] missing 2,3,5.

Now, in top-left subgrid, missing 3,5,6 for cells (1,2), (1,3), (2,2)

Also, (2,3) is 4, which is present.

Now, row2 has (2,2) and (2,5), (2,6) unknown.

But (2,2) is in top-left subgrid.

Similarly, row1 (1,2) and (1,3) in top-left.

Now, let's see possible numbers for (1,2).

(1,2) cannot be 1,2,4 (row1 has 2,4; col2 has row4=2, row6=4, but row1 col2 unknown, so col2 missing numbers.

Col2: row1=?, row2=?, row3=?, row4=2, row5=?, row6=4

Present: 2,4, so missing 1,3,5,6.

(1,2) must be one of 1,3,5,6, but row1 missing 1,3,5,6, so possible.

Similarly for others.

Now, in top-left subgrid, cells (1,2), (1,3), (2,2) must be {3,5,6}.

Also, (2,2) is in row2, which missing 2,3,5, so (2,2) can be 3 or 5 (since 2 not in {3,5,6}, but {3,5,6} for subgrid, but row2 missing 2,3,5, so (2,2) can be 3 or 5, not 6 because if (2,2)=6, but row2 missing 2,3,5, 6 is not missing, row2 has 1,4,6, so missing 2,3,5, so (2,2) must be 2,3, or 5.

But in subgrid, (2,2) must be in {3,5,6}, so intersection: 3 or 5.

Similarly, (1,2) must be in {3,5,6} and row1 missing 1,3,5,6, so possible 3,5,6.

Col2 missing 1,3,5,6, so no restriction.

Similarly for (1,3).

But let's see if we can find more.

Look at row4: [4,2,?,3,?,1]

Missing numbers: row4 has 4,2,?,3,?,1, so present: 1,2,3,4, missing 5,6.

So (4,3) and (4,5) must be 5 and 6 in some order.

(4,3) is row4 col3, which is in middle-left subgrid.

Middle-left subgrid: rows 3-4, cols 1-3, cells: (3,1)=6, (3,2)=?, (3,3)=1, (4,1)=4, (4,2)=2, (4,3)=?

Present: 6,1,4,2, so missing 3,5.

And (3,2) and (4,3) are unknown.

Now, (4,3) must be 5 or 6 from row4, but row4 missing 5 and 6, so (4,3) could be 5 or 6.

But in subgrid, missing 3 and 5, so (4,3) must be 5, because 6 is present in subgrid ( (3,1)=6), so (4,3) cannot be 6, must be 5.

Subgrid middle-left present: 6,1,4,2, so missing 3 and 5.

(4,3) is in this subgrid, and must be one of missing, so 3 or 5.

But from row4, (4,3) must be 5 or 6, but 6 is already in subgrid, so (4,3) cannot be 6, thus must be 5.

Yes.

So row4 col3 = 5.

Then, since row4 missing 5 and 6, and (4,3)=5, so (4,5) must be 6.

Row4: [4,2,5,3,?,1] so (4,5) must be 6.

Yes.

So (4,5) = 6.

Now, row4 is complete: [4,2,5,3,6,1]

Now, middle-right subgrid: rows 3-4, cols 4-6

(3,4)=?, (3,5)=?, (3,6)=?, (4,4)=3, (4,5)=6, (4,6)=1

Present: 3,6,1, so missing 2,4,5.

(3,4), (3,5), (3,6) unknown.

Also, row3: [6,?,1,?,?,?] missing 2,3,4,5 (since 6,1 present).

Col4: row1=?, row2=6, row3=?, row4=3, row5=2, row6=?

Row5 col4=2, from earlier? Row5: [5,?,?,2,?,?] so (5,4)=2.

Col4: row1=?, row2=6, row3=?, row4=3, row5=2, row6=?

Present: 6,3,2, so missing 1,4,5.

Similarly, col5: row1=4, row2=?, row3=?, row4=6, row5=?, row6=?

Present: 4,6, missing 1,2,3,5.

Row1 col5=4, row4 col5=6.

Back to row3.

Row3: [6,?,1,?,?,?] missing 2,3,4,5.

(3,2) is in middle-left subgrid, which we have.

Middle-left subgrid: we have (4,3)=5, so missing 3, and (3,2) must be 3.

Because missing 3 and 5, but 5 is now (4,3), so (3,2) must be 3.

Yes.

So row3 col2 = 3.

Now row3: [6,3,1,?,?,?] so missing 2,4,5 for (3,4),(3,5),(3,6)

Also, in middle-right subgrid, missing 2,4,5 for (3,4),(3,5),(3,6)

Now, col4: missing 1,4,5, and (3,4) is one of them.

Similarly, col5: missing 1,2,3,5, and (3,5) is one.

Now, row5 col4=2, which is present in col4.

Now, let's list row3 missing: positions (3,4), (3,5), (3,6) must be 2,4,5.

Now, possible for (3,4): can be 2,4,5 but col4 missing 1,4,5, so (3,4) can be 4 or 5 (since 2 is in row5, but not necessarily conflict, col4 has row5=2, so (3,4) cannot be 2 because row5 col4=2, so col4 has 2, so (3,4) cannot be 2, must be 4 or 5.

Similarly, (3,5): col5 missing 1,2,3,5, and row3 missing 2,4,5, so (3,5) can be 2 or 5 (4 not in col5 missing, but col5 has row1=4, so present 4, so (3,5) cannot be 4).

Col5: row1=4, row2=?, row3=?, row4=6, row5=?, row6=?

Present: 4,6, so missing 1,2,3,5.

Thus (3,5) can be 1,2,3,5, but row3 missing 2,4,5, and 4 not possible, so (3,5) can be 2 or 5.

Similarly, (3,6) must be the remaining.

Also, subgrid middle-right missing 2,4,5.

Now, (3,4) must be 4 or 5.

If (3,4)=4, then col4 has (3,4)=4, but col4 missing 1,4,5, so if (3,4)=4, then missing 1 and 5 for col4.

But row5 col4=2, row4 col4=3, row2 col4=6, row1 col4=?, row6 col4=?

Similarly, if (3,4)=5, then etc.

Also, row2 col4=6.

Now, let's see top-right subgrid.

Top-right subgrid: rows 1-2, cols 4-6

(1,4)=?, (1,5)=4, (1,6)=?, (2,4)=6, (2,5)=?, (2,6)=?

Present: 4,6, so missing 1,2,3,5.

Now, row1: [2,?,?,?,4,?] missing 1,3,5,6 for (1,2),(1,3),(1,6) since (1,1)=2, (1,5)=4.

Positions: (1,2), (1,3), (1,6) missing 1,3,5,6.

But (1,6) is in top-right subgrid.

Similarly, row2: [1,?,4,6,?,?] missing 2,3,5 for (2,2),(2,5),(2,6)

(2,5) and (2,6) in top-right subgrid.

Now, (1,5)=4 is in row1 and col5, which is present.

Back to (2,2).

(2,2) in top-left subgrid, which must be 3 or 5.

Also, (2,2) in row2, missing 2,3,5, so can be 3 or 5.

If (2,2)=3, then in top-left, (1,2) and (1,3) must be 5 and 6.

If (2,2)=5, then (1,2) and (1,3) must be 3 and 6.

Also, row1 (1,2) must be from {3,5,6}, etc.

Now, let's consider col3.

Col3: row1=?, row2=4, row3=1, row4=5, row5=?, row6=?

Present: 4,1,5, so missing 2,3,6.

(1,3) and (5,3), (6,3) must be 2,3,6.

But (1,3) is in top-left subgrid, which for (1,3), in subgrid missing 3,5,6, and row1 missing 1,3,5,6, so (1,3) can be 3,5,6.

But from col3 missing, (1,3) can be 2,3,6, so intersection: 3 or 6 (5 not in col3 missing).

Col3 missing 2,3,6, so (1,3) can be 2,3,6.

But in top-left subgrid, (1,3) must be in {3,5,6}, so possible 3 or 6 (2 not in {3,5,6}).

Similarly, if (1,3)=3 or 6.

Now, similarly for (1,2).

(1,2) in col2, missing 1,3,5,6, and subgrid {3,5,6}, and row1 missing 1,3,5,6, so all possible.

But let's see if we can find a contradiction or something.

Another point: row6 col2=4, row4 col2=2, etc.

Let's consider bottom rows.

Row5: [5,?,?,2,?,?] missing 1,3,4,6 (since 5,2 present).

Row6: [3,4,?,?,?,?] missing 1,2,5,6 (3,4 present).

But row6 col3=?, and in bottom-left subgrid.

Bottom-left subgrid: rows 5-6, cols 1-3

(5,1)=5, (5,2)=?, (5,3)=?, (6,1)=3, (6,2)=4, (6,3)=?

Present: 5,3,4, missing 1,2,6.

So (5,2), (5,3), (6,3) must be 1,2,6.

Now, row5 missing 1,3,4,6 for (5,2),(5,3),(5,5),(5,6)

But (5,2) and (5,3) are in this subgrid, must be from 1,2,6.

Similarly, (5,5) and (5,6) in bottom-right subgrid.

Row6 missing 1,2,5,6 for (6,3),(6,4),(6,5),(6,6), but (6,3) in bottom-left, must be from 1,2,6.

Now, col2: row1=?, row2=?, row3=3 (we have), row4=2, row5=?, row6=4

Present: 3,2,4, so missing 1,5,6.

Thus (1,2) and (2,2) and (5,2) must be 1,5,6.

But (1,2) and (2,2) are in top-left, which requires them to be from 3,5,6 for the missing, but with constraints.

From col2 missing 1,5,6, so (1,2), (2,2), (5,2) are 1,5,6 in some order.

But (5,2) is also in bottom-left subgrid, which requires (5,2) to be from 1,2,6.

So for (5,2), it must be in {1,2,6} from subgrid, and from col2 missing 1,5,6, so intersection: 1 or 6 (2 not in {1,5,6} for col2, but col2 missing 1,5,6, so (5,2) can be 1 or 6.

Similarly, from subgrid, 1 or 6, good.

Now, back to top.

Let's consider (2,2).

(2,2) must be 3 or 5 from earlier.

But from col2, (2,2) must be one of 1,5,6.

But 3 is not in {1,5,6}, so (2,2) cannot be 3, must be 5.

Because if (2,2)=3, but 3 is not in col2 missing, col2 missing 1,5,6, so (2,2) must be 1,5, or 6, not 3.

Therefore, (2,2) cannot be 3, so must be 5.

Then, since (2,2)=5, in top-left subgrid, missing 3,5,6, so (2,2)=5, thus (1,2) and (1,3) must be 3 and 6.

Now, row2: (2,2)=5, so row2: [1,5,4,6,?,?] missing 2 and 3 for (2,5) and (2,6).

Also, in top-left subgrid, (1,2) and (1,3) are 3 and 6.

Now, row1: (1,2) and (1,3) are 3 and 6, and (1,6) missing.

Row1 missing 1,3,5,6, but (1,2) and (1,3) are 3 and 6, so the remaining missing are 1 and 5 for (1,6) and... row1 has (1,1)=2, (1,2)=? , (1,3)=? , (1,4)=? , (1,5)=4, (1,6)=?

So after (1,2) and (1,3) are 3 and 6, then missing for row1: 1 and 5, for (1,4) and (1,6).

(1,4) and (1,6) must be 1 and 5.

Now, (1,4) is in top-right subgrid, and (1,6) also.

Top-right subgrid missing 1,2,3,5.

Now, similarly, (1,4) must be 1 or 5.

But col4 missing 1,4,5, and (1,4) can be 1 or 5.

Similarly, (1,6) must be the other of 1 or 5.

Now, let's see row3.

Row3: [6,3,1,?,?,?] missing 2,4,5.

And (3,4), (3,5), (3,6) must be 2,4,5.

Now, (3,4) must be 4 or 5, as earlier.

Also, (3,5) must be 2 or 5.

But if (3,4)=4, then (3,5) can be 2 or 5, and (3,6) the other.

If (3,4)=5, then (3,5) can be 2, and (3,6)=4, etc.

Now, col4: missing 1,4,5.

If (3,4)=4, then col4 has 4, missing 1 and 5.

If (3,4)=5, then missing 1 and 4.

Similarly, (1,4) must be 1 or 5.

If (3,4)=4, then (1,4) cannot be 4, must be 1 or 5.

Similarly, if (3,4)=5, then (1,4) cannot be 5, must be 1 or 4, but row1 (1,4) must be 1 or 5, so if (3,4)=5, then (1,4) must be 1.

Similarly for other cases.

Also, row2 missing 2 and 3 for (2,5) and (2,6).

(2,5) and (2,6) in top-right subgrid.

Top-right subgrid missing 1,2,3,5.

(2,5) and (2,6) must be 2 and 3, since row2 missing 2 and 3.

Row2 missing 2 and 3, so (2,5) and (2,6) are 2 and 3.

Then, in top-right subgrid, with (1,4), (1,6), (2,5), (2,6) must be 1,2,3,5.

But (2,5) and (2,6) are 2 and 3, so the missing are 1 and 5 for (1,4) and (1,6).

Which matches what we have for row1.

Now, (1,4) and (1,6) are 1 and 5.

Now, col4 missing 1,4,5.

If (1,4)=1, then col4 has 1, missing 4 and 5.

If (1,4)=5, then col4 has 5, missing 1 and 4.

Similarly, for (3,4).

Now, let's consider (3,4).

(3,4) must be 4 or 5.

Case 1: (3,4)=4.

Then col4 has (3,4)=4, so missing 1 and 5.

Then (1,4) must be 1 or 5, but since missing 1 and 5, possible.

Also, since (3,4)=4, then in row3, (3,5) and (3,6) must be 2 and 5, since missing 2,4,5 but (3,4)=4, so (3,5) and (3,6) are 2 and 5.

(3,5) must be 2 or 5.

If (3,5)=2, then (3,6)=5.

If (3,5)=5, then (3,6)=2.

Now, col5: missing 1,2,3,5.

(3,5) is 2 or 5.

If (3,5)=2, then col5 has 2, missing 1,3,5.

If (3,5)=5, then col5 has 5, missing 1,2,3.

Also, row5 col5=?, etc.

But let's see the other possibility for (3,4).

First, assume (3,4)=4.

Then (1,4) must be 1 or 5.

But in col4, with (3,4)=4, missing 1 and 5, so (1,4) can be 1 or 5.

Similarly, (1,6) the other.

Now, row5: [5,?,?,2,?,?] missing 1,3,4,6.

Col2 missing 1,5,6, and (5,2) must be 1 or 6, as earlier.

Similarly, bottom-left subgrid: (5,2), (5,3), (6,3) must be 1,2,6.

(5,2) is 1 or 6.

If (5,2)=1, then (5,3) and (6,3) must be 2 and 6.

If (5,2)=6, then (5,3) and (6,3) must be 1 and 2.

Now, row5 (5,3) must be from 1,2,6, and row5 missing 1,3,4,6 for (5,2),(5,3),(5,5),(5,6), so (5,3) can be 1 or 6 if (5,2) is not, but related.

Also, col3 missing 2,3,6, and (5,3) is in col3, so (5,3) must be 2,3, or 6.

But from subgrid, (5,3) must be from 1,2,6, so intersection: 2 or 6 (3 not in 1,2,6).

So (5,3) can be 2 or 6.

Similarly, if (5,3)=2, then from subgrid, if (5,2)=1, then (6,3)=6; if (5,2)=6, then (6,3)=1.

If (5,3)=6, then if (5,2)=1, (6,3)=2; if (5,2)=6, not possible because subgrid must have unique, so if (5,3)=6, then (5,2) cannot be 6, must be 1, and (6,3)=2.

Similarly, etc.

But let's go back to top.

Perhaps we can use the fact that (1,4) and (1,6) are 1 and 5.

Now, row6: [3,4,?,?,?,?] missing 1,2,5,6.

Col3 missing 2,3,6, but row6 col3=?, must be from bottom-left subgrid 1,2,6, and col3 missing 2,3,6, so (6,3) can be 2 or 6 (1 not in missing).

Col3 missing 2,3,6, so (6,3) must be 2 or 6.

From subgrid, (6,3) must be 1,2, or 6, but 1 not in col3 missing, so (6,3) must be 2 or 6.

Similarly, if (6,3)=2, then from subgrid, (5,2) and (5,3) must be 1 and 6.

If (6,3)=6, then (5,2) and (5,3) must be 1 and 2.

But (5,2) must be 1 or 6, so if (6,3)=6, then (5,2) cannot be 6, must be 1, and (5,3)=2.

Similarly, if (6,3)=2, then (5,2) and (5,3) are 1 and 6.

Now, let's assume (3,4)=4.

Then (3,5) and (3,6) are 2 and 5.

Also, (3,5) must be 2 or 5.

If (3,5)=2, then col5 has 2, missing 1,3,5.

If (3,5)=5, then col5 has 5, missing 1,2,3.

Now, similarly, for (1,4), if (3,4)=4, then (1,4) can be 1 or 5.

But let's see if we can find a value.

Another point: row2 (2,5) and (2,6) are 2 and 3.

(2,5) in col5, which missing 1,2,3,5.

If (2,5)=2, then col5 has 2, missing 1,3,5.

If (2,5)=3, then col5 has 3, missing 1,2,5.

But (2,5) is either 2 or 3.

Similarly, (2,6) the other.

Now, let's consider the bottom.

Perhaps start from row5.

Row5 col5=?, missing 1,3,4,6.

Col5 missing 1,2,3,5.

So (5,5) must be in missing for both, so can be 1,3,4,6 intersect 1,2,3,5, so 1 or 3.

Similarly, (5,6) must be the remaining.

But let's list all.

I think I need to systematically try possibilities or find a better way.

Let's list all empty cells with possibilities.

First, grid:

Row1: Col1=2, Col2=?, Col3=?, Col4=?, Col5=4, Col6=?
Row2: Col1=1, Col2=5, Col3=4, Col4=6, Col5=?, Col6=?
Row3: Col1=6, Col2=3, Col3=1, Col4=?, Col5=?, Col6=?
Row4: Col1=4, Col2=2, Col3=5, Col4=3, Col5=6, Col6=1
Row5: Col1=5, Col2=?, Col3=?, Col4=2, Col5=?, Col6=?
Row6: Col1=3, Col2=4, Col3=?, Col4=?, Col5=?, Col6=?

Now, row1: missing 1,3,5,6 for Col2,Col3,Col4,Col6, but with constraints.

From earlier, (1,2) and (1,3) are 3 and 6, and (1,4) and (1,6) are 1 and 5.

So for row1:

• (1,2): 3 or 6
• (1,3): the other of 3 or 6
• (1,4): 1 or 5
• (1,6): the other of 1 or 5

Similarly, row2: (2,5) and (2,6) are 2 and 3.

So (2,5): 2 or 3, (2,6): the other.

Row3: (3,4), (3,5), (3,6) are 2,4,5.

With (3,4): 4 or 5
(3,5): 2 or 5
(3,6): the remaining.

Row5: missing 1,3,4,6 for (5,2),(5,3),(5,5),(5,6)

But (5,2) must be 1 or 6 (from col2 and subgrid)
(5,3) must be 2 or 6 (from col3 and subgrid)

Also from bottom-left subgrid, (5,2), (5,3), (6,3) are 1,2,6.

Row6: missing 1,2,5,6 for (6,3),(6,4),(6,5),(6,6)

But (6,3) must be 2 or 6 (from col3 and subgrid)

Col4: missing 1,4,5
Col5: missing 1,2,3,5

Now, let's start with (3,4).

Suppose (3,4) = 4.

Then (3,5) and (3,6) are 2 and 5.

Also, since (3,4)=4, col4 has 4, so missing 1 and 5.

Then (1,4) must be 1 or 5, but since missing 1 and 5, possible.

Similarly, (1,6) the other.

Now, if (3,4)=4, then in middle-right subgrid, (3,4)=4, present, so missing 2,5 for (3,5),(3,6), and (4,5)=6 already, so (3,5) and (3,6) are 2 and 5.

(3,5) can be 2 or 5.

If (3,5)=2, then (3,6)=5.

Col5 has (3,5)=2, so missing 1,3,5.

If (3,5)=5, then col5 has 5, missing 1,2,3.

Also, row2 (2,5) is 2 or 3.

If (3,5)=2, then (2,5) cannot be 2, must be 3, and (2,6)=2.

Similarly, if (3,5)=5, then (2,5) can be 2 or 3.

But let's see the bottom.

Assume (3,4)=4 and (3,5)=2.

Then (3,6)=5.

Col5 has (3,5)=2, so missing 1,3,5.

Row2 (2,5) must be 3 (since 2 is taken), so (2,5)=3, (2,6)=2.

Then top-right subgrid: (2,5)=3, (2,6)=2, (1,4) and (1,6) are 1 and 5.

Also, (1,5)=4 present.

Now, (1,4) and (1,6) are 1 and 5.

Col4 missing 1 and 5, so no issue.

Now, row1 (1,4) can be 1 or 5.

Similarly, (1,6) the other.

Now, row5: (5,2) must be 1 or 6.

(5,3) must be 2 or 6.

But from bottom-left, (5,2), (5,3), (6,3) are 1,2,6.

If (5,2)=1, then (5,3) and (6,3) are 2 and 6.

If (5,2)=6, then (5,3) and (6,3) are 1 and 2.

But (5,3) must be 2 or 6, so if (5,2)=6, then (5,3) cannot be 6, must be 2, and (6,3)=1.

Similarly, if (5,2)=1, then (5,3) can be 2 or 6.

Col3 missing 2,3,6.

(5,3) must be 2 or 6.

(6,3) must be 2 or 6, but different.

Also, row6 (6,3) must be 2 or 6.

Suppose (5,2)=1, then (5,3) can be 2 or 6.

If (5,3)=2, then (6,3)=6.

If (5,3)=6, then (6,3)=2.

Both possible.

Now, similarly, row5 (5,5) and (5,6) missing.

Row5 missing 1,3,4,6, but (5,2)=1, so missing 3,4,6 for (5,3),(5,5),(5,6).

But (5,3) is 2 or 6, not 3 or 4, so (5,3) is 2 or 6, then (5,5) and (5,6) must be 3 and 4, or 3 and 6, but missing 3,4,6, and (5,3) takes one of 2 or 6, but 2 not in missing, missing are 3,4,6 for the cells.

Row5 cells: (5,2)=1, (5,3)=? , (5,4)=2, (5,5)=?, (5,6)=?

Missing values: 3,4,6 for (5,3),(5,5),(5,6)

But (5,3) must be 2 or 6 from earlier constraint, but 2 is not in missing values, missing are 3,4,6, so (5,3) cannot be 2, must be 6.

Because if (5,3)=2, but 2 is already in row5 at (5,4), so row5 cannot have duplicate, (5,4)=2, so (5,3) cannot be 2.

Therefore, (5,3) must be 6.

Then, since (5,3)=6, and missing values, so (5,5) and (5,6) must be 3 and 4.

From bottom-left, if (5,3)=6, and (5,2)=1, then (6,3) must be 2.

Also, (5,3)=6, which is consistent.

Then row5: (5,5) and (5,6) are 3 and 4.

Col5 missing 1,3,5, but we have (3,5)=2, so col5 has 2, missing 1,3,5.

(5,5) must be 3 or 4, but col5 missing 1,3,5, so (5,5) can be 3.

If (5,5)=3, then col5 has 3, missing 1 and 5.

If (5,5)=4, but 4 not in col5 missing, col5 has row1=4, row4=6, row3=2, so present 4,6,2, missing 1,3,5, so (5,5) cannot be 4, must be 3.

Then (5,6)=4.

Similarly, (5,5)=3, (5,6)=4.

Now, row6: (6,3)=2, as above.

Then row6 missing 1,5,6 for (6,4),(6,5),(6,6) since (6,1)=3, (6,2)=4, (6,3)=2, so missing 1,5,6.

Also, bottom-right subgrid: rows 5-6, cols 4-6

(5,4)=2, (5,5)=3, (5,6)=4, (6,4)=?, (6,5)=?, (6,6)=?

Present: 2,3,4, so missing 1,5,6.

So (6,4), (6,5), (6,6) must be 1,5,6.

And row6 missing 1,5,6, perfect.

Now, col4 missing 1,4,5, but we have (3,4)=4, so col4 has 4, missing 1 and 5.

(6,4) must be one of 1,5,6, but col4 missing 1 and 5, so (6,4) can be 1 or 5.

Similarly, col5 missing 1,3,5, but (5,5)=3, so col5 has 3, missing 1 and 5.

(6,5) must be in 1,5,6, so can be 1 or 5.

Col6: row1=?, row2=2 (since (2,6)=2), row3=5, row4=1, row5=4, row6=?

Row2 (2,6)=2, row3 (3,6)=5, row4 (4,6)=1, row5 (5,6)=4, so col6 present: 2,5,1,4, missing 3,6.

Row1 (1,6) must be 1 or 5, but col6 missing 3,6, so (1,6) cannot be 1 or 5, contradiction?

Col6: values present: row2=2, row3=5, row4=1, row5=4, so 2,5,1,4 present, missing 3 and 6.

Row1 col6= (1,6) must be 1 or 5 from row1, but 1 and 5 are already in col6? Row4 col6=1, row3 col6=5, so 1 and 5 are present, so (1,6) cannot be 1 or 5, must be 3 or 6.

But from row1, (1,6) must be 1 or 5, contradiction.

Therefore, our assumption that (3,4)=4 and (3,5)=2 is wrong.

Now, back to (3,4)=4, but (3,5) could be 5.

So case 2: (3,4)=4, (3,5)=5, then (3,6)=2.

Then col5 has (3,5)=5, so missing 1,2,3.

Row2 (2,5) can be 2 or 3.

If (2,5)=2, then (2,6)=3.

If (2,5)=3, then (2,6)=2.

Now, col6 missing 3,6 as before.

Row1 (1,6) must be 1 or 5.

But if (2,6)=2 or 3, etc.

Also, row5 same as before.

But let's not complicate.

Since we had contradiction with (3,5)=2, try (3,5)=5 with (3,4)=4.

So (3,4)=4, (3,5)=5, (3,6)=2.

Then col5 has 5, missing 1,2,3.

Row2 (2,5) can be 2 or 3.

Suppose (2,5)=2, then (2,6)=3.

Then top-right: (2,5)=2, (2,6)=3, (1,4) and (1,6) are 1 and 5.

Col6: row2=3, row3=2, row4=1, row5=4 (since row5 (5,6) not yet, but row5 (5,6) is one of missing).

Col6 present: row2=3, row3=2, row4=1, so 3,2,1 present, missing 4,5,6.

Row1 (1,6) must be 1 or 5, but 1 present, so cannot be 1, must be 5.

Then (1,4)=1.

Similarly, if (2,5)=3, then (2,6)=2, then col6 row2=2, row3=2 duplicate, impossible.

So only possibility: (2,5)=2, (2,6)=3, (1,6)=5, (1,4)=1.

Then row1: (1,2) and (1,3) are 3 and 6, say (1,2)=3 or 6, (1,3)= other.

Col2 missing 1,5,6, but (1,2) is 3 or 6, but 3 not in missing, missing 1,5,6, so (1,2) must be 6.

Then (1,3)=3.

Similarly, row1: (1,4)=1, (1,6)=5.

Now, col3: (1,3)=3, row2=4, row3=1, row4=5, so present 3,4,1,5, missing 2,6.

(5,3) and (6,3) must be 2 and 6.

Row5: (5,2) must be 1 or 6, but col2 missing 1,5,6, (1,2)=6, so col2 has 6, missing 1 and 5.

(5,2) must be 1 or 5, but from subgrid, 1 or 6, so must be 1 (since 6 taken).

Then (5,2)=1.

Then bottom-left: (5,2)=1, so (5,3) and (6,3) must be 2 and 6.

But col3 missing 2,6, so (5,3) can be 2 or 6.

If (5,3)=2, then (6,3)=6

If (5,3)=6, then (6,3)=2

Row5 missing 3,4,6 for (5,3),(5,5),(5,6) since (5,2)=1, (5,4)=2, so missing 3,4,6.

(5,3) must be 2 or 6, but 2 not in missing, missing 3,4,6, so (5,3) must be 6.

Then (6,3)=2.

Then row5 (5,5) and (5,6) are 3 and 4.

Col5 missing 1,2,3, but (3,5)=5, so missing 1,2,3.

(5,5) must be 3 or 4, but 4 not in missing, so (5,5) must be 3.

Then (5,6)=4.

Similarly, row6: (6,3)=2, so missing 1,5,6 for (6,4),(6,5),(6,6)

Col4 missing 1,4,5, but (3,4)=4, so missing 1 and 5.

(6,4) must be 1 or 5.

Similarly, col5 missing 1,2,3, (5,5)=3, so missing 1 and 2.

(6,5) must be 1 or 2.

But row6 missing 1,5,6, so (6,5) can be 1.

Bottom-right subgrid: (5,4)=2, (5,5)=3, (5,6)=4, (6,4)=?, (6,5)=?, (6,6)=? missing 1,5,6.

So (6,4), (6,5), (6,6) are 1,5,6.

Now, (6,4) must be 1 or 5 (col4 missing 1,5)

(6,5) must be 1 or 2 (col5 missing 1,2)

But row6 missing 1,5,6, so (6,5) can be 1.

If (6,5)=1, then col5 has 1, missing 2, but (6,5)=1, then missing 2 for col5, but row6 (6,5)=1, then (6,4) and (6,6) are 5 and 6.

Col5 missing 2, so (6,5) must be 2, but 2 not in {1,5,6} for row6, row6 missing 1,5,6, so (6,5) cannot be 2, must be 1 or 5 or 6, but from col5, must be 1 or 2, so must be 1.

Then (6,5)=1.

Then col5 has 1, missing 2.

Then (6,4) must be 5 or 6, but col4 missing 1 and 5, so (6,4) must be 5 (since 1 is for (6,5)).

Then (6,6)=6.

Similarly, all set.

But (6,4)=5, (6,5)=1, (6,6)=6.

Now, row1 col6=5, but we have (1,6)=5.

Col6: row1=5, row2=3, row3=2, row4=1, row5=4, row6=6, so 5,3,2,1,4,6 all present, good.

Similarly, other columns.

Now, we have (3,4)=4, but earlier we assumed (3,4)=4 for this case.

In this derivation, we had no contradiction.

But earlier with (3,5)=2 we had issue, but with (3,5)=5 it worked.

In the beginning, we had two cases for (3,4), we tried (3,4)=4 with (3,5)=5.

Now, what about (3,4)=5?

But since we have a solution, we can output it.

Let's write the full grid.

From above:

Row1: (1,1)=2, (1,2)=6 (since must be 6), (1,3)=3, (1,4)=1, (1,5)=4, (1,6)=5

Row2: (2,1)=1, (2,2)=5, (2,3)=4, (2,4)=6, (2,5)=2 (since we set), (2,6)=3

Row3: (3,1)=6, (3,2)=3, (3,3)=1, (3,4)=4, (3,5)=5, (3,6)=2

Row4: (4,1)=4, (4,2)=2, (4,3)=5, (4,4)=3, (4,5)=6, (4,6)=1

Row5: (5,1)=5, (5,2)=1, (5,3)=6, (5,4)=2, (5,5)=3, (5,6)=4

Row6: (6,1)=3, (6,2)=4, (6,3)=2, (6,4)=5, (6,5)=1, (6,6)=6

Now, check subgrids.

Top-left: (1,1)=2, (1,2)=6, (1,3)=3, (2,1)=1, (2,2)=5, (2,3)=4 → 1,2,3,4,5,6 good.

Top-right: (1,4)=1, (1,5)=4, (1,6)=5, (2,4)=6, (2,5)=2, (2,6)=3 → 1,4,5,6,2,3 all good.

Middle-left: (3,1)=6, (3,2)=3, (3,3)=1, (4,1)=4, (4,2)=2, (4,3)=5 → 6,3,1,4,2,5 good.

Middle-right: (3,4)=4, (3,5)=5, (3,6)=2, (4,4)=3, (4,5)=6, (4,6)=1 → 4,5,2,3,6,1 good.

Bottom-left: (5,1)=5, (5,2)=1, (5,3)=6, (6,1)=3, (6,2)=4, (6,3)=2 → 5,1,6,3,4,2 good.

Bottom-right: (5,4)=2, (5,5)=3, (5,6)=4, (6,4)=5, (6,5)=1, (6,6)=6 → 2,3,4,5,1,6 good.

Rows and columns all have 1-6.

So this is the solution.