Very Large Print Sudoku Puzzles for Seniors: 100 Easy Sudoku for ... - Free Printable

Let's solve this 4×4 Sudoku puzzle step by step.

---

🔍 Understanding the Rules

In a 4×4 Sudoku:
- Each row must contain the numbers 1, 2, 3, 4 exactly once.
- Each column must contain the numbers 1, 2, 3, 4 exactly once.
- Each of the four 2×2 subgrids (called "boxes") must also contain the numbers 1, 2, 3, 4 exactly once.

We are given:

```
+----+----+----+----+
| 4 | | | |
+----+----+----+----+
| | 1 | | 3 |
+----+----+----+----+
| | | | |
+----+----+----+----+
| 1 | | 3 | |
+----+----+----+----+
```

We'll label the grid with positions for clarity:

```
Row 1: [4, _, _, _]
Row 2: [_, 1, _, 3]
Row 3: [_, _, _, _]
Row 4: [1, _, 3, _]
```

---

Step 1: Look at Row 1

Row 1 has: `4, _, _, _` → missing: 1, 2, 3

But look at Column 1:
- Row 1: 4
- Row 2: ?
- Row 3: ?
- Row 4: 1

So Column 1 already has 4 and 1 → needs 2 and 3.

Now look at Box 1 (top-left 2×2):

```
[4, _]
[_, 1]
```

This box has 4 and 1 → needs 2 and 3.

So the empty cells in Box 1 (positions (1,2) and (2,1)) must be 2 and 3.

Let’s consider possibilities.

---

Step 2: Use Column 1

Column 1:
- R1: 4
- R2: ?
- R3: ?
- R4: 1

So missing: 2 and 3.

So R2C1 and R3C1 must be 2 and 3 in some order.

But from Box 1, we know that:
- (1,2) and (2,1) must be 2 and 3.

So:
- (2,1) = R2C1 → must be either 2 or 3
- (1,2) = R1C2 → must be the other

Let’s see if we can find more constraints.

---

Step 3: Look at Row 2

Row 2: [?, 1, ?, 3] → missing: 2, 4

So the two blanks in Row 2 must be 2 and 4.

So R2C1 and R2C3 must be 2 and 4.

But earlier, R2C1 must be 2 or 3 (from Column 1).

But now, R2C1 must be 2 or 4 (from Row 2).

The only common possibility is 2.

✔ So R2C1 = 2

Then:
- From Row 2: R2C3 must be 4
- From Column 1: R3C1 must be 3 (since 2 and 3 were missing, and 2 is used)
- From Box 1: since (2,1)=2, then (1,2) must be 3

So far:
- R2C1 = 2
- R2C3 = 4
- R3C1 = 3
- R1C2 = 3

Update the grid:

```
Row 1: [4, 3, _, _]
Row 2: [2, 1, 4, 3]
Row 3: [3, _, _, _]
Row 4: [1, _, 3, _]
```

Wait! Row 2 now has: 2, 1, 4, 3 → all good ✔

Check Column 2:
- R1: 3
- R2: 1
- R3: ?
- R4: ?

So missing: 2 and 4

Also check Box 2 (top-right 2×2):
- R1C3, R1C4
- R2C3=4, R2C4=3

So Box 2 has: ?, ?, 4, 3 → needs 1 and 2

But Row 1: [4, 3, ?, ?] → missing 1 and 2

So R1C3 and R1C4 must be 1 and 2.

But Box 2 needs 1 and 2 → matches.

So R1C3 and R1C4 = 1 and 2 in some order.

Now look at Column 3:
- R1: ?
- R2: 4
- R3: ?
- R4: 3

So missing: 1 and 2

So R1C3 and R3C3 must be 1 and 2.

Similarly, Column 4:
- R1: ?
- R2: 3
- R3: ?
- R4: ?

Missing: 1, 2, 4 — but R1C4 is one of 1 or 2, so 4 must go somewhere.

Wait — Column 4:
- R1: ?
- R2: 3
- R3: ?
- R4: ?

So missing: 1, 2, 4

R1C4 is either 1 or 2 → okay

Now back to Row 1: [4, 3, ?, ?] → need 1 and 2

So R1C3 and R1C4 = 1 and 2

Now, Column 3: R1C3 = 1 or 2, R2C3=4, R3C3=?, R4C3=3

So Column 3 has: ?, 4, ?, 3 → missing: 1 and 2

So R1C3 and R3C3 must be 1 and 2 → consistent.

Now let’s look at Row 4: [1, ?, 3, ?]

Missing: 2 and 4

So R4C2 and R4C4 must be 2 and 4

Now Column 2: R1=3, R2=1, R3=?, R4=?

Missing: 2 and 4 → so R3C2 and R4C2 = 2 and 4

But R4C2 must be 2 or 4 → same

Now, R4C2 is one of 2 or 4

And R3C2 is the other.

Now let’s look at Box 3 (bottom-left 2×2):

Rows 3-4, Columns 1-2

Current:
- R3C1 = 3
- R3C2 = ?
- R4C1 = 1
- R4C2 = ?

So values: 3, ?, 1, ?

Missing: 2 and 4

So R3C2 and R4C2 must be 2 and 4 → matches what we had.

Now, Row 4: [1, ?, 3, ?] → missing 2 and 4

So R4C2 and R4C4 = 2 and 4

So possible:
- R4C2 = 2 → R4C4 = 4
- or R4C2 = 4 → R4C4 = 2

But Column 4: R1C4 = 1 or 2, R2C4 = 3, R3C4 = ?, R4C4 = ?

Missing: 1, 2, 4

If R4C4 = 4 → then R1C4 and R3C4 must be 1 and 2

But R1C4 is already 1 or 2 → okay

If R4C4 = 2 → then R1C4 and R3C4 must be 1 and 4 → but R1C4 is only 1 or 2 → so cannot be 4 → contradiction!

So R4C4 cannot be 2 → must be 4

Therefore:
- R4C4 = 4
- Then R4C2 = 2 (since Row 4 missing 2 and 4)

So:
- R4C2 = 2
- R4C4 = 4

Now update:

Row 4: [1, 2, 3, 4] ✔

Now Column 2:
- R1: 3
- R2: 1
- R3: ?
- R4: 2

So missing: 4 → R3C2 = 4

Now Column 4:
- R1: ?
- R2: 3
- R3: ?
- R4: 4

Missing: 1 and 2

R1C4 is 1 or 2 → okay

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

Missing: 1 and 2

So R3C3 and R3C4 must be 1 and 2

Now Column 3:
- R1: ?
- R2: 4
- R3: ?
- R4: 3

Missing: 1 and 2 → so R1C3 and R3C3 = 1 and 2

Now Row 1: [4, 3, ?, ?] → missing 1 and 2 → so R1C3 and R1C4 = 1 and 2

Now we have:

- R1C3 and R1C4 = 1 and 2
- R3C3 and R3C4 = 1 and 2

But Column 3: R1C3 and R3C3 = 1 and 2 → okay

Column 4: R1C4 and R3C4 = 1 and 2 → okay

Now let’s use Box 2 (top-right): R1C3, R1C4, R2C3=4, R2C4=3

Needs 1 and 2 → so R1C3 and R1C4 = 1 and 2 → good

Now, which one goes where?

Try possibilities.

Suppose R1C3 = 1 → then R1C4 = 2

Then Column 3: R1C3 = 1, R2C3 = 4, R3C3 = ?, R4C3 = 3 → missing 2 → so R3C3 = 2

Then Row 3: R3C3 = 2 → so R3C4 = 1 (since Row 3 missing 1 and 2)

Now Column 4: R1C4 = 2, R2C4 = 3, R3C4 = 1, R4C4 = 4 → all present: 2,3,1,4 → ✔

Now check Box 4 (bottom-right): R3C3=2, R3C4=1, R4C3=3, R4C4=4 → values: 2,1,3,4 → all good ✔

Now check Row 3: [3, 4, 2, 1] → all unique → ✔

Row 1: [4, 3, 1, 2] → ✔

Now check columns:

- Col 1: 4,2,3,1 → all good
- Col 2: 3,1,4,2 → good
- Col 3: 1,4,2,3 → good
- Col 4: 2,3,1,4 → good

Boxes:
- Box 1: [4,3; 2,1] → 4,3,2,1 → good
- Box 2: [1,2; 4,3] → 1,2,4,3 → good
- Box 3: [3,4; 1,2] → 3,4,1,2 → good
- Box 4: [2,1; 3,4] → 2,1,3,4 → good

All constraints satisfied!

---

✔ Final Solution:

```
+----+----+----+----+
| 4 | 3 | 1 | 2 |
+----+----+----+----+
| 2 | 1 | 4 | 3 |
+----+----+----+----+
| 3 | 4 | 2 | 1 |
+----+----+----+----+
| 1 | 2 | 3 | 4 |
+----+----+----+----+
```

---

📌 Answer:

The completed Sudoku grid is:

```
4 3 1 2
2 1 4 3
3 4 2 1
1 2 3 4
```