Diamond Problems Worksheet Download - Free Printable

Let's solve each Diamond Problem step by step.

🔷 What is a Diamond Problem?

A diamond problem has four sections:
- Top: Product of the two side numbers
- Bottom: Sum of the two side numbers
- Left and Right: Two numbers (unknowns in these problems)

Given any two values, you can find the missing ones using:
- Top = Left × Right
- Bottom = Left + Right

We’ll use this rule to solve each diamond.

---

1)

```
50
/ \
? 5
\ /
?
```
We know:
- Top = 50
- Right = 5

So:
- Left = 50 ÷ 5 = 10
- Bottom = 10 + 5 = 15

✔ Answer: 10 and 15

---

2)

```
200
/ \
? 10
\ /
?
```
- Top = 200
- Right = 10
- Left = 200 ÷ 10 = 20
- Bottom = 20 + 10 = 30

✔ Answer: 20 and 30

---

3)

```
119
/ \
? 7
\ /
?
```
- Top = 119
- Right = 7
- Left = 119 ÷ 7 = 17
- Bottom = 17 + 7 = 24

✔ Answer: 17 and 24

---

4)

```
63
/ \
? 7
\ /
?
```
- Top = 63
- Right = 7
- Left = 63 ÷ 7 = 9
- Bottom = 9 + 7 = 16

✔ Answer: 9 and 16

---

5)

```
?
/ \
15 6
\ /
?
```
- Left = 15, Right = 6
- Top = 15 × 6 = 90
- Bottom = 15 + 6 = 21

✔ Answer: 90 and 21

---

6)

```
?
/ \
19 ?
\ /
29
```
- Left = 19, Bottom = 29
- So Right = 29 − 19 = 10
- Top = 19 × 10 = 190

✔ Answer: 190 and 10

---

7)

```
?
/ \
18 ?
\ /
21
```
- Left = 18, Bottom = 21
- Right = 21 − 18 = 3
- Top = 18 × 3 = 54

✔ Answer: 54 and 3

---

8)

```
48
/ \
? 6
\ /
?
```
- Top = 48, Right = 6
- Left = 48 ÷ 6 = 8
- Bottom = 8 + 6 = 14

✔ Answer: 8 and 14

---

9)

```
?
/ \
? 2
\ /
16
```
- Right = 2, Bottom = 16
- Left = 16 − 2 = 14
- Top = 14 × 2 = 28

✔ Answer: 28 and 14

---

10)

```
?
/ \
14 ?
\ /
32
```
- Left = 14, Bottom = 32
- Right = 32 − 14 = 18
- Top = 14 × 18 = 252

✔ Answer: 252 and 18

---

11)

```
260
/ \
? 20
\ /
?
```
- Top = 260, Right = 20
- Left = 260 ÷ 20 = 13
- Bottom = 13 + 20 = 33

✔ Answer: 13 and 33

---

12)

```
?
/ \
6 ?
\ /
12
```
- Left = 6, Bottom = 12
- Right = 12 − 6 = 6
- Top = 6 × 6 = 36

✔ Answer: 36 and 6

---

13)

```
?
/ \
10 ?
\ /
22
```
- Left = 10, Bottom = 22
- Right = 22 − 10 = 12
- Top = 10 × 12 = 120

✔ Answer: 120 and 12

---

14)

```
?
/ \
3 5
\ /
?
```
- Left = 3, Right = 5
- Top = 3 × 5 = 15
- Bottom = 3 + 5 = 8

✔ Answer: 15 and 8

---

15)

```
?
/ \
2 ?
\ /
15
```
- Left = 2, Bottom = 15
- Right = 15 − 2 = 13
- Top = 2 × 13 = 26

✔ Answer: 26 and 13

---

✔ Final Answers:

| # | Missing Numbers (Top and Bottom) |
|---|----------------------------------|
| 1 | 10, 15 |
| 2 | 20, 30 |
| 3 | 17, 24 |
| 4 | 9, 16 |
| 5 | 90, 21 |
| 6 | 190, 10 |
| 7 | 54, 3 |
| 8 | 8, 14 |
| 9 | 28, 14 |
|10 | 252, 18 |
|11 | 13, 33 |
|12 | 36, 6 |
|13 | 120, 12 |
|14 | 15, 8 |
|15 | 26, 13 |

> ⚠️ Note: The answer format likely expects both missing values — typically top and bottom. But sometimes only one value is required depending on context. Based on the layout, it seems both are expected.

---

📝 Answer Key (for filling in):

1. 10, 15
2. 20, 30
3. 17, 24
4. 9, 16
5. 90, 21
6. 190, 10
7. 54, 3
8. 8, 14
9. 28, 14
10. 252, 18
11. 13, 33
12. 36, 6
13. 120, 12
14. 15, 8
15. 26, 13

You can now fill them into the "Answers" column accordingly!