Missing number | Number And Math Puzzle - BrainFans - Free Printable

Let's analyze the given grid to find the pattern and determine the number that replaces the '?'.

We are given a 4×4 grid:

```
7 3 6 2
2 8 5 4
1 1 2 4
4 2 1 ?
```

We need to find the value of the missing number in the bottom-right corner (last cell).

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Step 1: Look for patterns

Let’s examine rows, columns, or diagonals for any mathematical relationships.

#### Try checking columns:

Let’s look at each column and see if there’s a pattern.

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Column 1: 7, 2, 1, 4
→ 7 → 2 → 1 → 4
No obvious arithmetic pattern.

But let's check sums:
- Sum = 7 + 2 + 1 + 4 = 14

Column 2: 3, 8, 1, 2 → sum = 3+8+1+2 = 14

Column 3: 6, 5, 2, 1 → sum = 6+5+2+1 = 14

Column 4: 2, 4, 4, ? → sum = 2+4+4+? = 10 + ?

Wait! The first three columns sum to 14. So maybe column 4 should also sum to 14?

Then:
> 2 + 4 + 4 + ? = 14
> 10 + ? = 14
> ? = 4

So is the answer 4?

Let’s verify if this makes sense.

But wait — is this the only possible pattern?

Let’s check rows now.

---

Row 1: 7 + 3 + 6 + 2 = 18
Row 2: 2 + 8 + 5 + 4 = 19
Row 3: 1 + 1 + 2 + 4 = 8
Row 4: 4 + 2 + 1 + ? = 7 + ?

No clear row sum pattern.

But earlier we saw all column sums (except last) are 14.

Let’s confirm:

- Col 1: 7+2+1+4 = 14 ✔
- Col 2: 3+8+1+2 = 14 ✔
- Col 3: 6+5+2+1 = 14 ✔
- Col 4: 2+4+4+? = 10 + ? → so ? = 4 to make it 14

So if the pattern is that each column sums to 14, then the missing number is 4.

Is there another way to confirm?

Let’s try diagonals or other patterns.

Alternatively, could it be based on multiplication or some operation between cells?

Try looking at products?

Or perhaps row-wise operations?

Another idea: Maybe each row has a relationship with the next?

Let’s try something else.

Look at first row: 7, 3, 6, 2
Second row: 2, 8, 5, 4
Third: 1, 1, 2, 4
Fourth: 4, 2, 1, ?

Notice that in column 3, values go: 6, 5, 2, 1 → decreasing
But not helpful.

Wait — what if we consider sums across diagonals?

Top-left to bottom-right diagonal: 7, 8, 2, ? → 7+8+2+? = 17 + ?
Other diagonal: 2, 5, 1, 4 → 2+5+1+4 = 12 → no clear link.

Alternatively, think about multiplication or ratios?

Another idea: Perhaps each cell is derived from others?

But that might be too complex.

Let’s go back to the column sum idea.

We have:

- Column 1: 7+2+1+4 = 14
- Column 2: 3+8+1+2 = 14
- Column 3: 6+5+2+1 = 14
- Column 4: 2+4+4+? = 10 + ?

So if the pattern is that each column sums to 14, then ? = 4.

Now, is there a reason to believe this pattern?

Yes — because the first three columns do sum to 14. That’s a strong clue.

Could it be coincidence?

Let’s test for row sums:

- Row 1: 7+3+6+2 = 18
- Row 2: 2+8+5+4 = 19
- Row 3: 1+1+2+4 = 8
- Row 4: 4+2+1+? = 7+?

No consistent pattern.

What about sum of all numbers?

Total sum = sum of all columns = 14 × 4 = 56 (if column 4 also sums to 14)

But let’s compute total without the '?':

Sum of known numbers:

Row 1: 7+3+6+2 = 18
Row 2: 2+8+5+4 = 19
Row 3: 1+1+2+4 = 8
Row 4: 4+2+1+? = 7+?

Total = 18+19+8+(7+?) = 52 + ?

If total sum is 56, then ? = 4.

Same result.

Alternatively, maybe it’s a magic square type puzzle, but not quite — since not all rows/columns sum to same.

But columns do seem to sum to 14.

Let’s double-check if there's an alternative pattern.

Try pairwise relationships.

For example, in each column, is there a relationship between top and bottom?

Column 1: 7 → 2 → 1 → 4
No clear progression.

But notice:

In column 4: 2, 4, 4, ?

From top to bottom: 2 → 4 (×2), then 4 → 4 (×1), then 4 → ? — could be ×0.5? But not likely.

Alternatively, maybe alternating operations?

Not convincing.

Try looking at differences between rows.

But again, no clear trend.

Another idea: Could the last row be related to previous rows via some operation?

For instance, is there a pattern where each row is derived from the one above?

Row 1: 7, 3, 6, 2
Row 2: 2, 8, 5, 4
Row 3: 1, 1, 2, 4
Row 4: 4, 2, 1, ?

Check if any operation links them.

For example, from row 1 to row 2:

7 → 2 (–5)
3 → 8 (+5)
6 → 5 (–1)
2 → 4 (+2) → no clear rule.

From row 2 to row 3:

2 → 1 (–1)
8 → 1 (–7)
5 → 2 (–3)
4 → 4 (0) → not consistent.

From row 3 to row 4:

1 → 4 (+3)
1 → 2 (+1)
2 → 1 (–1)
4 → ? → ?

No clear pattern.

But going back — the column sum pattern is very strong.

All three columns already sum to 14. It’s highly likely that the fourth column is meant to follow the same rule.

Therefore, the missing number is:

> ? = 14 - (2 + 4 + 4) = 14 - 10 = 4

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✔ Final Answer: 4

The number that replaces the '?' is 4.

This maintains the pattern that each column sums to 14.