A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds had he in all?

Options

A. 9
B. 18
C. 27
D. 36

Explanation

To solve the problem, we need to determine the total number of birds in the bag based on the information given by the bird shooter. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( S \) = number of sparrows
- \( P \) = number of pigeons
- \( D \) = number of ducks

### Step 2: Set Up Equations
From the information provided:
1. "All sparrows but six" means that the total number of birds minus the number of sparrows equals six. Thus, we can write:
\[ P + D = 6 \quad \text{(Equation 1)} \]

2. "All pigeons but six" means that the total number of birds minus the number of pigeons equals six. Thus, we can write:
\[ S + D = 6 \quad \text{(Equation 2)} \]

3. "All ducks but six" means that the total number of birds minus the number of ducks equals six. Thus, we can write:
\[ S + P = 6 \quad \text{(Equation 3)} \]

### Step 3: Solve the Equations
Now we have three equations:
1. \( P + D = 6 \)
2. \( S + D = 6 \)
3. \( S + P = 6 \)

From Equation 1, we can express \( D \) in terms of \( P \):
\[ D = 6 - P \quad \text{(Equation 4)} \]

From Equation 2, we can express \( S \) in terms of \( D \):
\[ S = 6 - D \quad \text{(Equation 5)} \]

Substituting Equation 4 into Equation 5 gives:
\[ S = 6 - (6 - P) = P \]

Now we know \( S = P \).

### Step 4: Substitute Back
Substituting \( S \) back into Equation 3:
\[ P + P = 6 \implies 2P = 6 \implies P = 3 \]

Since \( S = P \), we also have:
\[ S = 3 \]

Now, substituting \( P \) back into Equation 4 to find \( D \):
\[ D = 6 - P = 6 - 3 = 3 \]

### Step 5: Calculate Total Birds
Now we have:
- \( S = 3 \)
- \( P = 3 \)
- \( D = 3 \)

Thus, the total number of birds is:
\[ S + P + D = 3 + 3 + 3 = 9 \]

### Conclusion
The total number of birds in the bag is **9**.

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