Number puzzles - Puzzles for interviews and competitive ... - Free Printable

Let's analyze the given grid:

```
| 1 | 4 | ? |
| 4 | 2 | 5 |
| 2 | 2 | 3 |
| 49 | 64 | 169 |
```

We are to find the missing number in the top-right corner (the question mark).

Step 1: Observe the structure

The grid has 4 rows and 3 columns. The first three rows contain numbers, and the fourth row contains squares of numbers:
- 49 = 7²
- 64 = 8²
- 169 = 13²

So, it seems that the bottom row might be derived from some operation involving the numbers above.

Let’s label the grid as follows:

```
Row 1: 1 4 ?
Row 2: 4 2 5
Row 3: 2 2 3
Row 4: 49 64 169
```

Let’s look at each column separately and see if we can find a pattern.

---

Column 1:

Numbers: 1, 4, 2 → Bottom value: 49

Try combining 1, 4, 2 to get 49.

Note: 49 = 7²

Can we make 7 from 1, 4, 2?

Try:
- 1 + 4 + 2 = 7 → Yes!
Then 7² = 49 ✔

So, possible rule: Sum of the first three rows in a column → square of that sum = bottom value

Let’s test this on Column 2.

---

Column 2:

Numbers: 4, 2, 2 → Sum = 4 + 2 + 2 = 8 → 8² = 64 ✔

Matches the bottom value.

Now Column 3:
Numbers: ?, 5, 3 → Sum = ? + 5 + 3 = ? + 8

Bottom value is 169 = 13²

So: (? + 8) = 13 → ? = 5

Therefore, the missing number is 5

---

Final Answer: 5

Explanation:

Each column has three numbers in the top three rows. Their sum is squared to give the bottom number.

- Col 1: 1 + 4 + 2 = 7 → 7² = 49
- Col 2: 4 + 2 + 2 = 8 → 8² = 64
- Col 3: ? + 5 + 3 = 13 → So ? = 5 → 13² = 169

✔ All match.

Answer: 5 ✔