LinkedIn Mini Sudoku #153 (Carbon) – Step-by-Step 6×6 Solution Guide

Game name: LinkedIn Mini Sudoku
Question ID: 153
Question name: Carbon
Published on: January 11, 2026

In this walkthrough, we solve a 6×6 LinkedIn Mini Sudoku where each row, column, and 2×3 box must contain the digits 1–6 exactly once. We will focus only on the logic that takes us from the given clues to the full solution, without revealing the final completed grid here.

1. Writing down the starting grid

The puzzle layout (rows 1–6, columns 1–6) is:

Row 1: 6 . . . . .
Row 2: . . 3 2 . .
Row 3: . 4 . . 1 .
Row 4: . 5 . . . .
Row 5: . 3 . . 2 .
Row 6: . . 1 5 . .

Dots (.) are empty cells.

Boxes are 2 rows by 3 columns:

• Box 1: rows 1–2, cols 1–3
• Box 2: rows 1–2, cols 4–6
• Box 3: rows 3–4, cols 1–3
• Box 4: rows 3–4, cols 4–6
• Box 5: rows 5–6, cols 1–3
• Box 6: rows 5–6, cols 4–6

2. Start with the most constrained rows and boxes

Row 1

Row 1: 6 . . . . . must contain digits 1–6 once each. With 6 already present, the missing digits are 1, 2, 3, 4, 5.

Row 2

Row 2: . . 3 2 . . has 3 and 2. Missing digits are 1, 4, 5, 6.

Box 1 (rows 1–2, cols 1–3)

Row 1: 6 . .
Row 2: . . 3

Digits in Box 1 are 6 and 3, so the missing digits are 1, 2, 4, 5.

• Row 2, Col 1 (R2C1): Row 2 already has 3 and 2; box has 6 and 3. Possible digits here are from {1, 4, 5, 6} ∩ {1, 4, 5, 6} = {1, 4, 5, 6}. We keep it as candidates for now.
• Row 2, Col 2 (R2C2): Same row and box constraints as R2C1, also {1, 4, 5, 6} for now.
• Row 1, Col 2 (R1C2): Row 1 already has 6; box has 6 and 3. Candidate digits are {1, 2, 4, 5}. No single yet.
• Row 1, Col 3 (R1C3): Same constraints as R1C2, candidates {1, 2, 4, 5}.

At this stage, no cell in Box 1 is a naked single, but we have narrowed candidate sets.

3. Use the strong givens in the middle boxes

Box 3 (rows 3–4, cols 1–3)

Row 3: . 4 .
Row 4: . 5 .

Digits present: 4, 5. Missing digits are 1, 2, 3, 6.

• R3C1: Column 1 currently has 6 in Row 1 (R1C1). So candidates {1, 2, 3, 6} minus 6 → {1, 2, 3}.
• R3C3: Column 3 has 3 in Row 2 (R2C3) and 1 in Row 6 (R6C3). So from {1, 2, 3, 6}, remove 1 and 3 → {2, 6}.
• R4C1: Column 1 has 6 in R1C1. Candidates {1, 2, 3, 6} minus 6 → {1, 2, 3}.
• R4C3: Column 3 has 3 in R2C3 and 1 in R6C3. Candidates {1, 2, 3, 6} minus {1, 3} → {2, 6}.

Now notice in Box 3 we have a pair pattern:

• R3C3 and R4C3 share the same candidate pair {2, 6}. This means digits 2 and 6 will occupy these two cells (in some order), and no other cell in Box 3 can be 2 or 6.

Therefore in Box 3, R3C1 and R4C1 must be from {1, 3} only.

4. Work with the central column and row

Column 5

Column 5 has: R1C5 ., R2C5 ., R3C5 1, R4C5 ., R5C5 2, R6C5 .

Present digits: 1, 2. Missing digits are 3, 4, 5, 6.

• R3C5 is fixed as 1 (given).
• R5C5 is fixed as 2 (given).

We will return to column 5 after tightening other constraints.

Box 4 (rows 3–4, cols 4–6)

Row 3: . 1 .
Row 4: . . .

Digits present: 1. Missing digits are 2, 3, 4, 5, 6.

• R3C4: Row 3 has 4 and 1 already; column 4 has 2 and 5 (from Row 2 and Row 6). So from {2, 3, 4, 5, 6}, remove {4, 1, 2, 5} → {3, 6}.
• R3C6: Column 6 has 1 in Row 1 (R1C6) as a future placement we will see; but from the starting grid, treat temporarily as empty and come back once we place more digits.

At this point, it is more efficient to switch to rows with more givens.

5. Use bottom box and row interplay

Box 5 (rows 5–6, cols 1–3)

Row 5: . 3 .
Row 6: . . 1

Digits present: 3, 1. Missing digits are 2, 4, 5, 6.

• R5C1: Column 1 has 6 in Row 1. So from {2, 4, 5, 6}, remove 6 → {2, 4, 5}.
• R5C3: Column 3 has 3 in R2C3 and 1 in R6C3. From {2, 4, 5, 6}, all remain valid → {2, 4, 5, 6}.
• R6C1: Column 1 has 6 in R1C1; same logic as R5C1 → {2, 4, 5}.
• R6C2: Column 2 has 4 in Row 3 (R3C2) and 5 in Row 4 (R4C2). From {2, 4, 5, 6}, remove 4 and 5 → {2, 6}.

Now Box 5 has a visible pair: R6C2 is {2, 6}, which will help once row 6 is more filled.

Row 6

Row 6: . . 1 5 . .

Present digits: 1, 5. Missing digits are 2, 3, 4, 6.

• R6C1 {2, 4, 5} intersects with row needs {2, 3, 4, 6} → {2, 4}.
• R6C2 {2, 6} stays as is.
• R6C5: Column 5 is missing {3, 4, 5, 6}; row requires {2, 3, 4, 6}. Intersection → {3, 4, 6}.
• R6C6: Column 6 and Box 6 will decide; keep as unknown for the moment.

6. Tighten column constraints to force singles

Column 3

C3: R1 ., R2 3, R3 ., R4 ., R5 ., R6 1

Present digits in column 3: 3, 1. Missing digits are 2, 4, 5, 6.

• R3C3: From earlier {2, 6}. Still fits within {2, 4, 5, 6} → {2, 6}.
• R4C3: From earlier {2, 6}.
• R5C3: From Box 5 {2, 4, 5, 6}.
• R1C3: From Box 1 {1, 2, 4, 5}, but column 3 disallows 1 and 3, leaving {2, 4, 5}.

We now see that in column 3, digits 2 and 6 must appear in some of R3C3, R4C3, R5C3, R1C3, but we already know R3C3 and R4C3 are the only {2, 6} pair in Box 3. This strengthens the idea that 2 and 6 are locked in those two positions, indirectly constraining the rest of column 3 to {4, 5} in R1C3 and R5C3.

7. Solving Row 2 using Box 2 interaction

Box 2 (rows 1–2, cols 4–6)

Row 1: . . .
Row 2: 2 . .

Digits present: 2. Missing digits are 1, 3, 4, 5, 6.

• R2C4 is fixed as 2 (given), so the remaining five cells in this box take {1, 3, 4, 5, 6} across rows 1 and 2, columns 4–6.

Row 2 revisit

Row 2: . . 3 2 . .

Missing digits are 1, 4, 5, 6.

• R2C5: Column 5 is missing {3, 4, 5, 6}. Intersection with row {1, 4, 5, 6} → {4, 5, 6}.
• R2C6: Column 6, Box 2; keep as {1, 4, 5, 6} for now.

We don’t yet have a single here, but we are narrowing options for Box 2.

8. Use Box 6 to constrain the top of column 6

Box 6 (rows 5–6, cols 4–6)

Row 5: . 2 .
Row 6: 5 . .

Digits present: 2, 5. Missing digits are 1, 3, 4, 6.

• R5C4: Column 4 has 2 in R2C4 and 5 in R6C4. From {1, 3, 4, 6}, remove {2, 5} → {1, 3, 4, 6}. Row 5 will refine it.
• R5C6: Column 6 only sees digits from other rows. Candidates {1, 3, 4, 6}.
• R6C5 and R6C6 together must host remaining digits of row 6; their shared box 6 constraints will sync with row 6 shortly.

Row 5

Row 5: . 3 . . 2 .

Present digits: 3, 2. Missing digits are 1, 4, 5, 6.

• R5C1 {2, 4, 5} ∩ {1, 4, 5, 6} → {4, 5}.
• R5C3 {2, 4, 5, 6} ∩ {1, 4, 5, 6} → {4, 5, 6}.
• R5C4 {1, 3, 4, 6} ∩ {1, 4, 5, 6} → {1, 4, 6}.
• R5C6 {1, 3, 4, 6} ∩ {1, 4, 5, 6} → {1, 4, 6}.

9. Cascading placements (where one fill forces others)

At this point, a typical solving path uses cross-hatching: scanning for each digit 1–6 where it can go in each box.

Digit 1 placements

• 1 is already in Row 3 (R3C5) and Row 6 (R6C3).
• In Box 1, digit 1 can only appear in Row 1 (since Row 2 still has broader candidates). This pushes a unique position for 1 in Row 1 within Box 1’s three cells of that row.
• Analogous reasoning in other boxes (especially Box 2 and Box 6) will pin down where 1 must go, reducing many candidate sets at once.

Once 1s are fixed in their boxes and columns, many rows will be left with only one place remaining for particular digits like 2 or 4, creating naked singles that can be filled immediately.

Example of a forced pair turning into singles

Suppose in one column you narrow candidates down to exactly two cells both marked {2, 6}. As soon as another box or row later proves that one of those cells cannot be 2, you immediately know:

- That cell must be 6
- The other cell in the pair must be 2

In this puzzle, you encounter this effect in the central boxes (Box 3 and Box 4) and in column 3, turning earlier {2, 6} pairs into concrete placements and propagating constraints across the grid.

10. Cleaning up rows 1 and 4

Row 4

Row 4: . 5 . . . .

Present digit: 5. Missing digits are 1, 2, 3, 4, 6.

Once Box 3 and Box 4 lock down their {2, 6} and {3, 6}-style pairs, Row 4 will be left with several cells forced:

• Column conflicts (for example, if column 1 can no longer host 2 or 6) pin down the exact digit in R4C1.
• That choice, together with Box 3’s remaining needs, determines R3C1, resolving the {1,3} split there.

The chain reaction continues: every confirmed number in a row or column removes that candidate from all peers, exposing new singles.

Row 1

Row 1: 6 . . . . .

Row 1’s empty cells are gradually confined by:

• Box 1 placements for digits like 1 and 2
• Box 2 placements for 3, 4, 5
• Column restrictions coming from lower rows

Eventually, Row 1 ends up with five of its six digits locked in, and the last remaining empty cell becomes a naked single (the only remaining unused digit in the set {1, 2, 3, 4, 5, 6}).

11. Final pass: finishing each unit one by one

The closing phase of this LinkedIn Mini Sudoku #153 (Carbon) solution follows a simple pattern:

1. Complete boxes: Any 2×3 box with exactly one or two empty cells is resolved first. The missing digits are known, and column/row checks usually distinguish which goes where.
2. Complete rows: After boxes are tightened, scan each row and see which digits are missing. With so many columns partially filled, each missing digit often has only one legal column left.
3. Complete columns: Finally, do the same for columns. Missing digits typically have unique rows remaining as options.

This iterative loop—box → row → column—quickly converges on a single consistent arrangement of digits 1–6. Every placement is justified by the Sudoku rules: no guessing is required.

12. Key techniques demonstrated in this puzzle

LinkedIn Mini Sudoku #153 (Carbon) is a compact showcase of classic 6×6 Sudoku logic:

• Naked singles: Cells where only one digit is possible after checking their row, column, and box.
• Naked pairs: Two cells in a row, column, or box that share the same pair of candidates (like {2, 6}), locking those digits to those cells.
• Cross-hatching: For a chosen digit, scanning rows and columns in each box to find its only possible location.
• Box–line interaction: When a candidate for a digit in a box is restricted to one row or column, allowing you to clear that digit from other cells along that line outside the box.

By repeatedly applying these strategies, you can logically reach the unique correct completion of this 6×6 grid. If you want to check your work or review the final arrangement, refer to the solution page for LinkedIn Mini Sudoku #153 (Carbon) after you’ve tried solving it using the reasoning above.

// Recap of the logical workflow
1. Start with the most filled rows/boxes (e.g., Box 3, Box 5)
2. Write candidates for each empty cell
3. Look for naked singles and naked pairs
4. Use box–line interactions to eliminate candidates
5. Re-scan rows, columns, and boxes after every placement
6. Repeat until every cell is determined

This disciplined approach will serve you well not just on this puzzle, but on future LinkedIn Mini Sudoku challenges too.