Logic Puzzle

Alright, let's tackle this problem step by step. The question is:

"Sally (a girl) has 3 brothers. Each brother has 2 sisters. How many sisters does Sally have?"

At first glance, it might seem a bit confusing, but let's break it down to understand it better.

Understanding the Problem

We have a family with several children, and we're given information about Sally and her brothers. Here's what we know:

1. Sally is a girl.
2. Sally has 3 brothers.
3. Each brother has 2 sisters.

We need to determine: How many sisters does Sally have?

Breaking Down the Information

First, let's list out the children in the family based on the information given.

1. Sally: She is one girl in the family.
2. Sally's brothers: There are 3 brothers.

So far, we have:

• Girls: Sally
• Boys: Brother 1, Brother 2, Brother 3

Now, the next piece of information is: "Each brother has 2 sisters."

This means that if we take any one of the brothers, he has 2 sisters.

Determining the Sisters

Let's think about what "each brother has 2 sisters" implies.

• For Brother 1: He has 2 sisters.
• For Brother 2: He has 2 sisters.
• For Brother 3: He has 2 sisters.

Now, who are these sisters? They are the female children in the family.

We already know that Sally is one sister. If each brother has 2 sisters, and Sally is one of them, who is the other sister?

This suggests that there must be another girl in the family besides Sally to make the count of sisters equal to 2 for each brother.

Let's denote the other sister as "Sister 2."

Now, the family looks like:

• Girls: Sally, Sister 2
• Boys: Brother 1, Brother 2, Brother 3

Now, let's check if this satisfies the condition that each brother has 2 sisters.

• For any brother, his sisters are Sally and Sister 2. That's 2 sisters. This checks out.

Verifying the Number of Sisters Sally Has

Now, the question is asking: How many sisters does Sally have?

From our current family setup:

• Sally's siblings are: Brother 1, Brother 2, Brother 3, and Sister 2.

So, Sally has one sister (Sister 2).

But wait, let's double-check to ensure we haven't missed anything.

Re-evaluating the Family Structure

Initially, we thought:

• Sally is one girl.
• 3 brothers.
• Each brother has 2 sisters, implying another sister besides Sally.

But is it possible that Sally is the only sister, and the count is somehow different?

Let's explore that.

If Sally is the only sister:

• Sisters: Sally
• Brothers: 3

Then, each brother would have only 1 sister (Sally), but the problem states that each brother has 2 sisters. This doesn't match, so Sally cannot be the only sister.

Therefore, there must be at least one more sister besides Sally to make the count of sisters equal to 2 for each brother.

Considering More Sisters

Could there be more than one other sister? Let's see.

If there are two other sisters besides Sally (let's call them Sister 2 and Sister 3), then:

• Sisters: Sally, Sister 2, Sister 3
• Brothers: 3

Now, each brother would have 3 sisters, but the problem says each brother has 2 sisters. This is too many, so we can't have more than one other sister.

Therefore, the only possibility is:

• Sisters: Sally, Sister 2
• Brothers: 3

This gives each brother exactly 2 sisters (Sally and Sister 2), which matches the given information.

Final Count of Sally's Sisters

Now, the question is: How many sisters does Sally have?

Sally's siblings are:

• Brothers: 3
• Sisters: Sister 2

So, Sally has 1 sister.

Potential Missteps

Initially, one might think that since each brother has 2 sisters, and there are 3 brothers, there are 6 sister instances (3 brothers × 2 sisters each), leading to the idea that there are 6 sisters. But this would be incorrect because all brothers share the same sisters; the sisters aren't unique to each brother.

Another possible confusion is thinking that Sally is not included in the count of sisters for the brothers, leading to an incorrect addition. But Sally is indeed one of the sisters that the brothers have.

Conclusion

After carefully analyzing the family structure and ensuring that all given conditions are met, we conclude that:

Sally has 1 sister.