Six people A, B, C, D, E and F are sitting on the ground in a hexagonal shape. All the sides of the hexagon so formed are of same length. A is not adjacent to B or C, D is not adjacent to C or E, B and C are adjacent, F is in the middle of D and C.
Which of the following is not a correct neighbour pair?

Options

A. A and F
B. D and F
C. B and E
D. C and F

Explanation

To solve the problem, we need to arrange the six people (A, B, C, D, E, and F) in a hexagonal shape while adhering to the given conditions. Let's break down the steps:

### Step 1: Draw the Hexagon
We start by drawing a hexagon and labeling the vertices. The vertices will represent the positions of A, B, C, D, E, and F.

```
1
/ \
2 6
| |
3-----4
\ /
5
```

### Step 2: Place A
According to the conditions, A is not adjacent to B or C. We can place A at position 1.

```
A
/ \
2 6
| |
3-----4
\ /
5
```

### Step 3: Place B and C
Since B and C are adjacent, we can place them in positions 2 and 3. However, we need to ensure that A is not adjacent to either of them. Therefore, we can place B at position 2 and C at position 3.

```
A
/ \
B 6
| |
C-----4
\ /
5
```

### Step 4: Place D
D is not adjacent to C or E. Since C is at position 3, D cannot be at position 4. We can place D at position 6.

```
A
/ \
B D
| |
C-----4
\ /
5
```

### Step 5: Place F
F is in the middle of D and C. Since D is at position 6 and C is at position 3, F can be placed at position 5.

```
A
/ \
B D
| |
C-----F
\ /
5
```

### Step 6: Place E
The only position left is position 4, so we place E there.

```
A
/ \
B D
| |
C-----E
\ /
F
```

### Summary of Arrangement
1. A is at position 1
2. B is at position 2
3. C is at position 3
4. E is at position 4
5. F is at position 5
6. D is at position 6

### Step 7: Identify Incorrect Neighbor Pairs
Now we need to identify which of the following pairs is not a correct neighbor pair:
- A and F
- D and F
- B and E
- B and D
- C and F

From our arrangement:
- A is not adjacent to F (correct)
- D is adjacent to F (incorrect)
- B is adjacent to E (correct)
- B is adjacent to D (correct)
- C is adjacent to F (correct)

### Conclusion
The pair that is not a correct neighbor pair is **D and F**.

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