Question

The stolen pigeons

Bad Bargle sneaked into Homer's pigeon loft one day. He took half of the pigeons. He decided
that wasn't bad enough, so he took one more and left. Later, Homer opened the door of the
loft to exercise his prize possessions. Half of the remaining flock flew away, leaving only six
inside the pen. How many pigeons did Homer have before Bad Bargle did his dirty deed?
(only type in whole numbers, no decimals nor fractions!)
How many pigeons did Bad Bargle take away?
How many pigeons were there in the beginning?

Answer 1

Bad Bargle took away 27 pigeons. In the beginning, there were 52 pigeons.

Let's denote the original number of pigeons as
`\( P \)`.

1. Bad Bargle took half of the pigeons:

After this, Homer has
`\( (1)/(2) \)` of the pigeons.

Remaining pigeons:
`\( (1)/(2)P \)`

2. Bad Bargle took one more:

Now, Homer has
`\( (1)/(2)P - 1 \)` pigeons.

3. Later, half of the remaining flock flew away:

After this, Homer has
`\( (1)/(2) \)` of the remaining pigeons.

Remaining pigeons:
`\( (1)/(4)P - (1)/(2) \)`

But we know that there are only 6 pigeons left:

`\[ (1)/(4)P - (1)/(2) = 6 \]`

Solve for
`\( P \)`:

`\[ (1)/(4)P = 6 + (1)/(2) \]`

`\[ (1)/(4)P = (13)/(2) \]`

`\[ P = 13 * 4 \]`

`\[ P = 52 \]`

So, Homer originally had 52 pigeons.

Now, let's answer the specific questions:

How many pigeons did Bad Bargle take away?

Bad Bargle took away half of the pigeons initially and then one more, so he took
`\( (1)/(2)P + 1 \)` pigeons.

`\[ (1)/(2)(52) + 1 = 26 + 1 = 27 \]`

Bad Bargle took away 27 pigeons.

How many pigeons were there in the beginning?

In the beginning, there were
`\( P = 52 \)` pigeons.