What is the smallest number of ducks that could swim in this formation? "Two ducks in front of a duck, two ducks behind a duck and a duck between two ducks".

Options

A. 9
B. 7
C. 5
D. 3

Explanation

To solve the problem of finding the smallest number of ducks that could swim in the specified formation, we can break it down step by step:

### Step 1: Understand the Formation
The problem states:
- Two ducks in front of a duck.
- Two ducks behind a duck.
- A duck between two ducks.

### Step 2: Visualize the Arrangement
Let’s visualize the arrangement of the ducks based on the given conditions. We can denote the ducks as D1, D2, and D3.

1. **D1** is the first duck.
2. **D2** is the second duck.
3. **D3** is the third duck.

### Step 3: Analyze the Conditions
- If we consider **D2** as the duck that has two ducks in front of it, then **D1** and **D3** can be positioned accordingly.
- **D1** is in front of **D2**.
- **D3** is behind **D2**.

This satisfies the condition of having two ducks in front of **D2** (which is not possible since we only have three ducks). Therefore, we need to consider the arrangement that allows for two ducks behind and in front of a duck.

### Step 4: Arrange the Ducks
Now, let’s arrange them:
- **D1** (front)
- **D2** (middle)
- **D3** (back)

In this arrangement:
- **D1** and **D2** are in front of **D3**.
- **D2** and **D3** are behind **D1**.
- **D2** is between **D1** and **D3**.

### Step 5: Conclusion
Thus, the smallest number of ducks that can swim in this formation is **3**.

### Final Answer
The smallest number of ducks that could swim in this formation is **3**.

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