Find the missing number Try to... - Brain teasers and puzzles ... - Free Printable

Let's solve this math puzzle step by step.

We are given three hexagons, each divided into six triangular sections with numbers. The middle hexagon has a ? in the top triangle, and we need to find the missing number based on a pattern from the other two hexagons.

Let’s label the positions of the numbers in each hexagon for clarity:

Each hexagon has 6 segments:
- Top
- Top-right
- Bottom-right
- Bottom
- Bottom-left
- Top-left

We’ll denote them as:

```
A
F B
E C
D
```

So the layout is:

```
A
F B
E C
D
```

Let’s write down the values for each hexagon.

---

Hexagon 1:

```
7
3 4
7 8
4
```

So:
- A = 7 (top)
- B = 4 (top-right)
- C = 8 (bottom-right)
- D = 4 (bottom)
- E = 7 (bottom-left)
- F = 3 (top-left)

---

Hexagon 2 (missing number):

```
?
2 8
5 6
7
```

So:
- A = ? (we need to find)
- B = 8
- C = 6
- D = 7
- E = 5
- F = 2

---

Hexagon 3:

```
6
4 7
9 4
3
```

So:
- A = 6
- B = 7
- C = 4
- D = 3
- E = 9
- F = 4

---

Now, look for patterns. Let’s check if there’s a consistent rule across all three hexagons.

Try to find a relationship between the numbers.

One common type of puzzle involves sums or products across opposite sides.

Let’s try checking opposite pairs:

In a hexagon, opposite triangles are:
- A (top) ↔ D (bottom)
- B (top-right) ↔ E (bottom-left)
- C (bottom-right) ↔ F (top-left)

Let’s test this idea.

---

Hexagon 1:

- A = 7, D = 4 → 7 + 4 = 11
- B = 4, E = 7 → 4 + 7 = 11
- C = 8, F = 3 → 8 + 3 = 11

All opposite pairs sum to 11!

Interesting!

---

Hexagon 3:

- A = 6, D = 3 → 6 + 3 = 9
- B = 7, E = 9 → 7 + 9 = 16
- C = 4, F = 4 → 4 + 4 = 8

No consistency here — not all sum to same value.

But wait — maybe it's not addition?

Wait — let’s double-check.

Hexagon 1: All opposite pairs sum to 11

Now Hexagon 3:
- A = 6, D = 3 → 9
- B = 7, E = 9 → 16
- C = 4, F = 4 → 8

Not matching.

But maybe there's another pattern.

Wait — perhaps the sum of all six numbers is constant?

Let’s compute total sum per hexagon.

---

Hexagon 1:

3 + 7 + 4 + 8 + 4 + 7 =
3+7=10, +4=14, +8=22, +4=26, +7=33 → 33

Hexagon 2:

2 + ? + 8 + 6 + 7 + 5 =
2+8=10, +6=16, +7=23, +5=28 → 28 + ? → total = 28 + ?

Hexagon 3:

4 + 6 + 7 + 4 + 3 + 9 =
4+6=10, +7=17, +4=21, +3=24, +9=33 → 33

Oh! Hexagon 1 and Hexagon 3 both sum to 33.

So likely, Hexagon 2 should also sum to 33.

So:
Sum of known numbers in Hexagon 2:
2 (F) + 8 (B) + 6 (C) + 7 (D) + 5 (E) =
2+8=10, +6=16, +7=23, +5=28

So missing number (A) = 33 - 28 = 5

So the missing number is 5

Let’s verify if that makes sense.

If A = 5, then:

Hexagon 2:
- A = 5
- B = 8
- C = 6
- D = 7
- E = 5
- F = 2

Total: 5+8+6+7+5+2 = 33 ✔

Now, does this match any pattern like opposite pairs?

Check opposite pairs in Hexagon 2:
- A = 5, D = 7 → 5+7 = 12
- B = 8, E = 5 → 8+5 = 13
- C = 6, F = 2 → 6+2 = 8

Not consistent.

But since Hexagon 1 and Hexagon 3 both sum to 33, and Hexagon 2 must follow the same rule, it's very likely that the total sum is always 33.

Thus, the missing number is:

> 5

---

✔ Final Answer: 5

Explanation:

The sum of all six numbers in each hexagon is 33.

- Hexagon 1: 3+7+4+8+4+7 = 33
- Hexagon 3: 4+6+7+4+3+9 = 33
- So Hexagon 2: Missing number = 33 - (2+8+6+7+5) = 33 - 28 = 5

Therefore, the missing number is 5.