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 straightforward, but let's break it down to ensure we understand it correctly.

Understanding the Problem

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

1. Sally is a girl: This means Sally is one of the daughters in the family.
2. Sally has 3 brothers: So, there are three male siblings in the family.
3. Each brother has 2 sisters: This is a crucial piece of information. It tells us something about the total number of sisters in the family from each brother's perspective.

Our goal is to determine how many sisters Sally has.

Visualizing the Family

Sometimes, drawing a simple diagram or listing out the information can help. Let's try that.

Let's denote:

• Sally: S (female)
• Brothers: B1, B2, B3 (all male)

So, currently, we have:

• Sisters: S
• Brothers: B1, B2, B3

Now, the statement says "each brother has 2 sisters." Let's interpret what that means for one brother, say B1.

From B1's perspective:

• He is a brother, so he doesn't count himself as a sister.
• He has sisters: S (Sally) and possibly others.

But we're told he has 2 sisters. Currently, we only have S as a sister. So, where does the second sister come from?

This implies that there must be another sister besides Sally. Let's call this other sister S2.

Now, our family looks like:

• Sisters: S (Sally), S2
• Brothers: B1, B2, B3

Now, let's check if this fits the given information.

Verifying the Information

1. Sally has 3 brothers: Yes, B1, B2, B3.
2. Each brother has 2 sisters:
   • For B1: sisters are S and S2 → 2 sisters.
   • For B2: sisters are S and S2 → 2 sisters.
   • For B3: sisters are S and S2 → 2 sisters.

This checks out. Each brother indeed has 2 sisters.

Determining Sally's Sisters

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

From our current family structure:

• Sisters: S (Sally), S2
• Brothers: B1, B2, B3

Sally is one of the sisters. So, her sisters would be the other sisters in the family besides herself.

That is:

• Sally's sisters: S2

So, Sally has 1 sister.

Potential Missteps

Initially, one might think that since each brother has 2 sisters, and there are 3 brothers, the total number of sisters is 2 (because each brother counts the same sisters). However, this would imply that the number of sisters is independent of the number of brothers in terms of counting.

But the key is to realize that the sisters are shared among all brothers. That is, the sisters are the same for each brother. So, if each brother has 2 sisters, and all brothers share the same sisters, then the total number of sisters is 2 (including Sally).

But the question asks for how many sisters Sally has, not the total number of sisters in the family.

Sally is one sister, and there's another sister (S2), so Sally has 1 sister.

Alternative Approach

Let me think of it another way to confirm.

Let’s denote:

• Total sisters = S
• Total brothers = B

Given:

• Sally is a girl, so she is one of the sisters.
• Sally has 3 brothers: B = 3
• Each brother has 2 sisters: So, for each brother, number of sisters = 2

But the sisters are the same for all brothers. So, the total number of sisters is 2 (since each brother counts the same sisters).

But Sally is one of these sisters. So, the other sister is 2 (total sisters) - 1 (Sally) = 1.

Therefore, Sally has 1 sister.

Checking with Numbers

Let's assign numbers to see if it makes sense.

Suppose:

• Sisters: Sally (S), Sister X (SX)
• Brothers: Brother 1 (B1), Brother 2 (B2), Brother 3 (B3)

Now:

• Sally has 3 brothers: B1, B2, B3 → correct.
• Each brother has 2 sisters:
  • B1: S, SX → 2
  • B2: S, SX → 2
  • B3: S, SX → 2

This fits perfectly.

If we had only Sally as a sister:

• Sisters: Sally
• Brothers: B1, B2, B3 Then each brother would have only 1 sister (Sally), but the problem states each has 2 sisters. So, this can't be the case.

If we had Sally and two other sisters:

• Sisters: S, SX, SY
• Brothers: B1, B2, B3 Then each brother would have 3 sisters, which contradicts the given that each has 2.

So, the only configuration that fits is:

• Sisters: S, SX
• Brothers: B1, B2, B3

Thus, Sally has 1 sister (SX).

Conclusion

After carefully analyzing the problem from different angles and verifying each step, the correct answer is:

Sally has 1 sister.