24 / 06 / 18
June 2024, Alice in Wonderland Test
Inspired by Nezhurina et al. 2024 , I employ similar questions to evaluate various leading language models, demonstrating their reasoning capabilities. Thus, this blog will resemble a test report. This test is very subjective. So, if the outcome does not meet your expectations, just take it in stride.
1-Standard Prompt
1-1-Varation-1
💡 Alice has 3 sisters and she also has 4 brothers. How many sisters does Alice’s brother have?
ChatGPT-4
Alice's brother has 3 sisters. This is because Alice herself is a sister, and she has 3 other sisters, making a total of 4 sisters. However, from the perspective of any of her brothers, they would count Alice and her other 3 sisters as their sisters, not including themselves. Thus, Alice's brother has 3 sisters.
ChatGPT-4o
Alice’s brother has the same number of sisters as Alice. Since Alice has 3 sisters, her brother also has 3 sisters.
Qwen2-72B-instruct
Alice's brother has 3 sisters. The number of sisters Alice's brother has does not change based on the number of brothers Alice has. Regardless of how many brothers Alice has, her brothers only have the sisters that Alice also has, which is 3.
Qwen1.5-110B-Chat
Alice's brother has 4 sisters. This includes Alice and her 3 other sisters. When counting sisters from the perspective of Alice's brother, Alice is included in that count.
Claude-3-opus-2024-0229
Great! Let's solve this problem step by step. To find out how many sisters Alice's brother has, we need to consider the information given about Alice's family. Given: - Alice has 3 sisters. - Alice has 4 brothers. Step 1: Determine the total number of siblings Alice has. Total siblings = Number of sisters + Number of brothers Total siblings = 3 + 4 = 7 Step 2: From the perspective of one of Alice's brothers, determine the number of sisters he has. Number of sisters = Total number of Alice's sisters + Alice Number of sisters = 3 + 1 = 4 Therefore, each of Alice's brothers has 4 sisters.
Gemini-1.5-pro-api-0514
Alice's brother also has **3** sisters. They all share the same sisters.
Yi-large-preview
If Alice has 3 sisters, it means there are 4 girls in total (Alice + 3 sisters). Alice also has 4 brothers. Since the question asks for the number of sisters Alice's brother has, we can see that each brother would have the same number of sisters (since they share the same sisters). Therefore, each brother has 3 sisters.
DeepSeek-V2 Chat
Let's break down the problem: 1. Alice has 3 sisters. 2. Alice also has 4 brothers. Now, we want to find out how many sisters Alice's brother has. Since Alice's brothers are also brothers to Alice's sisters, the number of sisters that Alice's brother has is the same as the number of sisters Alice has, which is 3. So the answer is $\boxed{3}$.
glm-4-0520
If Alice has 3 sisters, this means that there are 4 girls in total when including Alice. Alice's brothers would also have these same 3 sisters. Therefore, Alice's brothers have 3 sisters. The number of brothers Alice has (which is 4) does not affect the number of sisters her brothers have.
im-a-good-gpt2-chatbot
To solve this problem, we need to determine how many sisters Alice's brother has. Alice has 3 sisters and 4 brothers. Considering one of Alice's brothers: - He has the same 3 sisters that Alice has (since they are all siblings). - He does not count himself as a sister, obviously. - He is not one of Alice's sisters. Therefore, each of Alice's brothers has the same number of sisters as Alice does. Thus, **Alice's brother has 3 sisters**.
In this section, although all models perform reasoning, only Qwen1.5-110B-Chat and Claude-3-opus-2024-0229 provide correct answers. Qwen1.5-110B-Chat is an open-source model from Alibaba, while Claude-3-opus-2024-0229 uses the classic CoT framework, even without any CoT triggers in the prompt. The other models made mistakes during reasoning.
1-2-Varation-2
💡 Alice has M sisters and she also has N brothers. How many sisters does Alice’s brother have?
ChatGPT-4
Alice has M sisters and N brothers. Each of Alice’s brothers would have M sisters as well, because they all share the same siblings. Therefore,Alice’s brother has M sisters.
ChatGPT-4o
Alice’s brother would have the same number of sisters as Alice, since both Alice and her brother share the same family members. Therefore, Alice’s brother has M sisters.
Qwen2-72B-instruct
Alice's brother has M sisters, the same number that Alice has sisters, because all of Alice's sisters are also the sisters of Alice's brother. The number of brothers Alice has (N) does not affect the number of sisters her brother has. So the answer is M.
Qwen1.5-110B-Chat
Alice's brother has M sisters. This is because Alice's siblings consist of M sisters and N brothers. Since Alice's brother is one of the N brothers, he shares the same M sisters as Alice.
Claude-3-opus-2024-0229
Let's organize the information we have: * Alice has M sisters * Alice has N brothers Now, let's think about this step by step: 1) Alice's brothers and sisters are siblings to each other. 2) So, each of Alice's brothers has the same number of sisters as Alice has. 3) The question is asking about the number of sisters that Alice's brother has. This is the same as the number of sisters Alice has. 4) We know that Alice has M sisters. Therefore, each of Alice's brothers also has M sisters.
Gemini-1.5-pro-api-0514
Alice's brother will have M sisters. Here's why: * They share the same sisters: If Alice has M sisters, and her brother is a sibling, he also shares those same M sisters.
Yi-large-preview
If Alice has M sisters, then she is one of the sisters to her brothers. So, each of her brothers has \(M-1\) sisters, since they don't count Alice as a sister to themselves but only as a sibling. Therefore, Alice's brother has \(M-1\) sisters. The number of brothers Alice has, N, does not affect this count.
DeepSeek-V2 Chat
Let's break down the problem: 1. Alice has M sisters. 2. Alice also has N brothers. We are asked to find out how many sisters Alice's brother has. Since Alice's brother is one of her N brothers, the sisters that Alice's brother has are the same as the sisters Alice has, because they share the same sisters. Therefore, Alice's brother has M sisters. So the answer is $\boxed{M}$.
glm-4-0520
She has M sisters, and since they are all siblings, each of her brothers has the same number of sisters. Therefore, each of Alice's brothers has M sisters. However, we must exclude Alice herself when considering the number of sisters from the perspective of her brothers. So, each brother would have M - 1 sisters. So the final answer is that Alice's brother has M - 1 sisters.
im-a-good-gpt2-chatbot
To determine how many sisters Alice's brother has, let's analyze the family structure described. Alice has \( M \) sisters and \( N \) brothers. 1. **Count Alice's Sisters:** Since the problem asks about Alice's brother, note that all of Alice's sisters are also his sisters. 2. **Include Alice:** In addition to her \( M \) sisters, each brother would also count Alice as a sister (since she is a female sibling). Therefore, each of Alice's brothers has \( M \) sisters from Alice's sisters and 1 additional sister (Alice herself). Thus, the total number of sisters that one of Alice's brothers has is: \[ M + 1 \] So, the answer is \( \boxed{M + 1} \).
In this section, although all these models perform reasoning, 'im-a-good-gpt2-chatbot' is the only one that gets the correct answer.. Despite rumors that this model originates from OpenAI, both ChatGPT-4 and ChatGPT-4o are unable to provide the correct answer.
2-Variation Prompt
In this section, I will not use the standard prompt. Instead, I will employ strategies like CoT, Self-Consistency, few-shot, and others to determine if the model can provide the correct response.
2-1-Variation-1 Two-shot
💡 Alice has 2 sisters and she also has3 brothers. How many sisters does Alice's brother have? ##Answer: 3 Alice has 4 sisters and she also has 2 brothers. How many sisters does Alice's brother have? ## Answer: 5 Alice has M sisters and she also has N brother. How many sisters does Alice’s brother have?
ChatGPT-4
In the problem, Alice has M sisters and N brothers. Each brother would have M sisters because they all share the same siblings. Hence, each of Alice’s brothers has M sisters.
ChatGPT-4o
Alice has M sisters and N brothers. Since all of Alice’s brothers share the same number of sisters as Alice does, each of Alice’s brothers has M sisters. Therefore, the number of sisters that Alice’s brother has is M.
Qwen2-72B-Instruct
Alice's brother has M sisters.
Qwen1.5-110B-Chat
If Alice has M sisters and N brothers, and we are asked to find out how many sisters Alice's brother has, the answer would be M-1, assuming that one of the siblings counted as a brother is the brother in question. However, in the context of the question, it's implied that we're not considering the brother himself as having a sister relationship with himself. So, for any given brother of Alice, the number of sisters he has is simply the total number of Alice's sisters, since he is not included in the count of sisters. So, the correct interpretation without specific numbers given would be: Alice's brother has M sisters.
Claude-3-opus-2024-0229
To find the number of sisters Alice's brother has, we need to consider the total number of siblings and subtract the number of brothers. Given: - Alice has M sisters. - Alice also has N brothers. Step 1: Calculate the total number of siblings Alice has. Total siblings = Number of sisters + Number of brothers Total siblings = M + N Step 2: Calculate the number of sisters Alice's brother has by subtracting the number of brothers (including himself) from the total number of siblings. Number of sisters Alice's brother has = Total siblings - Number of brothers Number of sisters Alice's brother has = (M + N) - (N + 1) Number of sisters Alice's brother has = M + N - N - 1 Number of sisters Alice's brother has = M - 1 Therefore, Alice's brother has M - 1 sisters.
Gemini-1.5-pro-api-0514
Here's how to break down the logic to find the answer: * **Alice's siblings:** Alice has M sisters and N brothers. * **From a brother's perspective:** Her brother would consider Alice as one of his sisters. * **Total sisters for the brother:** He has all of Alice's sisters, plus Alice herself. **Therefore, Alice's brother has M + 1 sisters.**
Yi-large-preview
To generalize the pattern you've observed: - In the first scenario, Alice has 2 sisters and 3 brothers. Alice's brother has 3 sisters (Alice and her 2 sisters). - In the second scenario, Alice has 4 sisters and 2 brothers. Alice's brother has 5 sisters (Alice and her 4 sisters). From these examples, we can see that Alice's brother has as many sisters as Alice has, plus Alice herself. So, if Alice has \(M\) sisters and \(N\) brothers, then Alice's brother has \(M+1\) sisters because he includes Alice in his count of sisters. The \(+1\) accounts for Alice herself, who is also his sister. Therefore, if Alice has \(M\) sisters and \(N\) brothers, Alice's brother has \(M+1\) sisters.
DeepSeek-V2 Chat
To solve this problem, we need to understand the relationship between the number of sisters Alice has and the number of sisters her brother has. 1. **Case 1**: Alice has 2 sisters and 3 brothers. - If Alice has 2 sisters, then each of her brothers also has 2 sisters (including Alice). 2. **Case 2**: Alice has 4 sisters and 2 brothers. - If Alice has 4 sisters, then each of her brothers also has 4 sisters (including Alice). 3. **General Case**: Alice has M sisters and N brothers. - If Alice has M sisters, then each of her brothers also has M sisters (including Alice). Therefore, for the general case where Alice has M sisters and N brothers, each of Alice's brothers has **M** sisters.
glm-4-0520
If Alice has M sisters and she also has N brothers, then Alice herself is not included in the count of siblings when considering how many sisters her brothers have. Since Alice's brothers are not counting Alice, the number of sisters that Alice's brothers have would be M, because all of Alice's sisters are also sisters to her brothers. Therefore, if Alice has M sisters and N brothers, Alice's brother has M sisters.
im-a-good-gpt2-chatbot
To determine how many sisters Alice's brother has, consider how siblings relate to each other in a family. If Alice has \( M \) sisters, she is one of \( M+1 \) girls in the family (including herself). Now, Alice has \( N \) brothers. Each of these brothers would have all the girls in the family as their sisters, except for themselves, obviously. But since they are not girls, each brother simply has all the girls (the \( M+1 \) girls) as sisters. Therefore, each of Alice's brothers has \( M+1 \) sisters. So, the number of sisters that Alice's brother has is \(\boxed{M+1}\).
When utilizing the two-shot prompt technique, we discover that both Yi-large-preview from 01-ai and Gemini-1.5-pro-api-0514 from Google answer the question correctly. I personally favor Yi-large-preview's response because it correctly analyzes and reasons the two examples provided. Surprisingly, both ChatGPT-4 and ChatGPT-4o from OpenAI fail to provide the correct answer. However, im-a-good-gpt2-chatbot delivers the right answer without any doubt.
2-2-Variation-2 Zero-Shot CoT
💡 Alice has M sisters and she also has N brothers. How many sisters does Alice’s brother have? Think it step by step.
ChatGPT-4
To find out how many sisters Alice’s brother has, we need to consider the family structure: 1. Total Sisters: Alice has M sisters. Therefore, including Alice, there are M + 1 females who are siblings in the family. 2. Siblings’ Perspective: From the perspective of any of Alice’s brothers, they would count all of their female siblings as sisters, except themselves. Since Alice’s brother would count Alice as a sister, and Alice has M other sisters, each brother has: M + 1 sisters in total. This count includes Alice and her M sisters.
ChatGPT-4o
To determine how many sisters Alice's brother has, let's break it down step-by-step. 1. **Identify the Total Number of Siblings**: Alice has \( M \) sisters and \( N \) brothers. Including Alice herself, the total number of children in the family is: \[ M \, \text{sisters} + N \, \text{brothers} + 1 \, \text{(Alice)} = M + N + 1 \, \text{(total children)} \] 2. **Count the Number of Sisters for Any Brother**: Each brother will have the same number of sisters. Since Alice is one of the sisters, and there are \( M \) sisters in total (including Alice), the number of sisters that each brother has is: \[ M \] Thus, Alice’s brother has \( M \) sisters.
Qwen2-72B-Instruct
To determine how many sisters Alice's brother has, let's break down the information given: 1. **Alice has M sisters.** This means that there are M female siblings other than Alice in the family. 2. **Alice has N brothers.** This means that there are N male siblings other than any hypothetical brother we are considering. Now, let's consider one of Alice's brothers. Since Alice's brother is also a part of the same family, he shares the same siblings as Alice. Therefore: - He has M sisters, which includes Alice and the M-1 other sisters Alice has. - He also has N-1 brothers, excluding himself. So, when we are asked how many sisters Alice's brother has, the answer is **M**, which includes Alice and all of Alice's other sisters.
Qwen1.5-110B-Chat
Let's break it down step by step: 1. Alice has M sisters. 2. Alice also has N brothers. Now, we're asked to find out how many sisters Alice's brother has. Since we're referring to a specific brother (one of the N brothers Alice has), we need to consider the family structure from his perspective. - From the information given, we know that Alice is one of the siblings who has both sisters and brothers. - When considering one of Alice's brothers, we understand that he shares all of Alice's sisters as his sisters too. Therefore, Alice's brother has the same number of sisters as Alice does, which is M sisters.
Claude-3-opus-2024-0229
Okay, let's think this through step by step: 1. Understand the given information: * Alice has M sisters. * Alice has N brothers. 2. Consider Alice's siblings from her brother's perspective: * Alice's brother is also a sibling to all of Alice's sisters and brothers, except for himself. 3. Count the number of sisters Alice's brother has: * Alice has M sisters, and all of them are also sisters to Alice's brother. * Therefore, Alice's brother has M sisters. 4. Verify the result: * Alice's brother has the same number of sisters as Alice, which is M. So, Alice's brother has M sisters.
Gemini-1.5-pro-api-0514
Here's how to solve this step-by-step: * **Alice's siblings:** Alice has M sisters and N brothers, so she has a total of M + N siblings. * **Her brother's siblings:** Since they are all siblings, Alice's brother also has M + N total siblings. * **Removing Alice:** However, we need to exclude Alice when counting the sisters of Alice's brother. This leaves M + N - 1 siblings. * **Counting only sisters:** Alice's brother still has the same number of sisters as Alice, which is M. **Therefore, Alice's brother has M sisters.**
Yi-large-preview
To solve this, let's break it down step by step: 1. Alice has M sisters. This means there are M+1 sisters in total, including Alice herself. 2. Alice has N brothers. This means there are N brothers in total. 3. The question is asking how many sisters Alice’s brother has. Since any brother of Alice (and there are N of them) will have the same sisters as Alice does, each brother will have M sisters. Therefore, Alice’s brother has M sisters.
DeepSeek-V2 Chat
To determine how many sisters Alice's brother has, we need to consider the siblings of Alice's brother. Since Alice's brother is one of Alice's N brothers, the sisters of Alice's brother are the same as the sisters Alice has, which is M. Therefore, Alice's brother has M sisters.
glm-4-0520
Let's break this down step by step: Alice has M sisters. This means that the total number of female siblings in the family, including Alice, is M. Since Alice is one of the sisters, the number of sisters that Alice has (excluding herself) would be M - 1. Now, Alice also has N brothers. Each of these brothers would have the same set of sisters as Alice because they all share the same parents. Therefore, each brother would have M - 1 sisters, the same number that Alice has, because we don't count Alice herself when we're considering the number of sisters from the perspective of one of her brothers. In conclusion, Alice’s brothers have M - 1 sisters each.
im-a-good-gpt2-chatbot
To determine how many sisters Alice's brother has, let's analyze the family structure step by step. 1. **Count Alice's Sisters and Brothers:** - Alice has \( M \) sisters. - Alice has \( N \) brothers. 2. **Include Alice in the Count:** - The total number of sisters as seen by any of Alice's brothers would be Alice herself plus her other \( M \) sisters. 3. **Calculate the Total Number of Sisters:** - Alice's brother would count Alice as a sister. - He would also count Alice's \( M \) other sisters. So, the total number of sisters that any of Alice's brothers has is: \[ M + 1 \] Thus, **Alice's brother has \( M + 1 \) sisters**. This includes Alice and her \( M \) sisters.
Zero-shot CoT is renowned for its "think step by step" approach. When using this, we find that only ChatGPT-4 provides the correct answer. Both Yi-large-preview and Gemini-1.5-pro-api-0514, which previously gave the correct answer in Two-shot, are now incorrect. Finally, im-a-good-gpt2-chatbot delivers the correct answer without any doubt.
2-3-Variation-3 One-Shot CoT
💡 Kitty has 4 sisters and she also has 3 brothers. How many sisters does Kitty’s brother have? Since Kitty’s brother should share same sisters with Kitty, except for Kitty. So we need to count Kitty as another sister for her brother as well. Therefore, Kitty’s brother has 4+1 = 5 sisters. Alice has M sisters and she also has N brothers. How many sisters does Alice’s brother have?
ChatGPT-4
For Alice, the situation is similar to Kitty's. Alice has \( M \) sisters, and \( N \) brothers. Each of Alice's brothers would have Alice as a sister, in addition to her \( M \) sisters. So, Alice's brother has \( M + 1 \) sisters in total.
ChatGPT-4o
In the case of Alice, let’s break down the problem step by step: 1. **Number of Sisters**: - Alice has \( M \) sisters. 2. **Number of Brothers**: - Alice has \( N \) brothers. 3. **Number of Sisters for Alice’s Brother**: - Each of Alice’s brothers shares the same sisters as Alice, which means they have \( M \) sisters. - Additionally, Alice herself is a sister to her brothers. Therefore, each of Alice’s brothers has \( M + 1 \) sisters (the \( M \) sisters plus Alice). So, the number of sisters that Alice’s brother has is \( M + 1 \).
Qwen2-72B-Instruct
Alice's brother would have M sisters, since he shares the same sisters as Alice, but we do not count Alice herself as a sister to her brother. Therefore, Alice’s brother has M sisters. However, if we want to include Alice as a sister for her brother, then Alice’s brother would have M+1 sisters. But typically, when we talk about the number of sisters a person has, we do not include that person as one of their own sisters.
Qwen1.5-110B-Chat
To determine how many sisters Alice's brother has, we follow a similar logic to the one used for Kitty. If Alice has M sisters and N brothers, then each of her brothers shares all her sisters but is not a sister to himself. Therefore, if we are considering the perspective of Alice's brother, he has M sisters because he counts all of Alice's sisters as his own, without adding Alice as an additional sister since the question's logic seems to be excluding the sibling in question when counting. So, Alice's brother has M sisters.
Claude-3-opus-2024-0229
Let's approach this problem step by step, just like we did in the example with Kitty. Given: - Alice has M sisters. - Alice also has N brothers. To find out how many sisters Alice's brother has, we need to consider the following: 1. Alice's brother shares the same sisters as Alice, except for Alice herself. 2. Since Alice is a sister to her brother, we need to count her as an additional sister. Therefore, the number of sisters Alice's brother has can be calculated as follows: - Number of sisters shared with Alice = M - Alice is an additional sister to her brother = 1 - Total number of sisters Alice's brother has = M + 1 So, Alice's brother has M + 1 sisters.
Gemini-1.5-pro-api-0514
You're absolutely right about how to solve this kind of problem! You need to count Alice herself as a sister to her brother. Here's the answer: Alice's brother has **M + 1** sisters.
Yi-large-preview
To determine how many sisters Alice's brother has, we follow the same logic applied in the case of Kitty. Alice has \(M\) sisters and \(N\) brothers. This means that each of Alice's brothers (since we're assuming they all have the same parents, and thus the same siblings) has \(M-1\) sisters, not counting Alice herself. However, when considering Alice's brother's perspective, we need to include Alice in the count of his sisters since she is a sister to him. Therefore, Alice's brother has \(M-1+1 = M\) sisters. This is because from Alice's perspective, she doesn't count herself in her number of sisters (M), but from her brother's perspective, he would count Alice among his sisters, thus keeping the total number of sisters he has equal to \(M\).
DeepSeek-V2 Chat
To find out how many sisters Alice's brother has, we can follow the same logic as in the example with Kitty. Alice has M sisters and N brothers. Since Alice's brother shares the same sisters as Alice, except for Alice herself, we need to include Alice as another sister for her brother. Therefore, Alice's brother has M + 1 sisters.
glm-4-0520
Applying the same logic used for Kitty's situation, if Alice has M sisters and N brothers, then Alice's brother would have M sisters. This is because Alice and all her sisters would be considered the sisters of her brothers. Therefore, we do not add 1 to the number of Alice's sisters when counting how many sisters Alice's brother has because Alice is already included in the count of M sisters. So, Alice's brother has M sisters.
im-a-good-gpt2-chatbot
To determine the number of sisters Alice's brother has, we follow the same logic as used in the Kitty example. Alice has \( M \) sisters and \( N \) brothers. Each of Alice's brothers would have the same sisters as Alice, plus Alice herself (since Alice is also a sister to her brothers). Therefore, the total number of sisters that each of Alice's brothers has is: \[ M + 1 \] So, Alice's brother has \( \boxed{M + 1} \) sisters.
In this section, we utilize one-shot CoT to enhance model performance. We discover that many models can successfully answer the question, with the exception of glm-4-0520, Yi-large-preview, Qwen2-72B-Instruct, and Qwen1.5-110B-Chat. Despite using one-shot CoT as a demonstration, these models still fail to answer the question correctly.
2-4-Variation-4 Self-Consistency
💡 Alice has M sisters and she also has N brothers. How many sisters does Alice’s brother have? Show five thinking methods. The final answer should be the one with the highest frequency.
ChatGPT-4
To find how many sisters Alice's brother has, we consider the following thought processes: ### 1. Basic Arithmetic Alice has \( M \) sisters and \( N \) brothers. Each of Alice's brothers would also have \( M \) sisters because all of Alice's sisters are their sisters too. They do not count Alice as an additional sister because she is their sibling, not an additional sister. Thus, each brother has \( M \) sisters. ### 2. Set Theory Let's represent the family as sets. The set of sisters \( S \) has \( M \) members, and the set of brothers \( B \) has \( N \) members. The intersection of these sets \( S \cap B \) is empty because no one can be both a brother and a sister. For any member of \( B \) (i.e., a brother), the count of his sisters is the size of \( S \), which is \( M \). ### 3. Diagramming Draw a family tree. Place Alice at the center, draw \( M \) lines connecting her to \( M \) sisters and \( N \) lines connecting her to \( N \) brothers. If you pick any one of the brother lines and follow it to count siblings excluding him, you still end up counting all \( M \) sisters. ### 4. Logical Reasoning Each brother of Alice considers all females among Alice's siblings as his sisters, except for himself. Since brothers do not count themselves as sisters and Alice is not an additional sister, each brother sees exactly \( M \) sisters. ### 5. Proof by Contradiction Assume that Alice's brother has a different number of sisters, say \( M' \) where \( M' \neq M \). If \( M' > M \), that would imply there are more sisters than accounted for, which is impossible since only \( M \) sisters exist. If \( M' < M \), some biological sisters are not counted, which is also incorrect. Hence, the only logical number is \( M \). **Conclusion:** All five methods conclude that each of Alice's brothers has \( M \) sisters. The method used most frequently in reasoning is logical reasoning and basic arithmetic. Thus, Alice's brother has \( M \) sisters.
ChatGPT-4o
Sure, let's explore five different thinking methods to solve the problem of how many sisters Alice's brother has: ### Method 1: Direct Reasoning 1. Alice has \( M \) sisters. 2. Alice is one of the sisters. 3. Therefore, Alice's \( M \) sisters are also the sisters of each of her brothers. 4. Each brother has \( M \) sisters. ### Method 2: Counting Family Members 1. Alice is one member of the family. 2. She has \( M \) sisters and \( N \) brothers. 3. Total number of girls (including Alice) is \( M + 1 \). 4. The number of sisters each brother has is \( M \) (excluding Alice in the count). ### Method 3: Subtracting Alice 1. Consider the total number of girls in the family \( M + 1 \) (including Alice). 2. Each brother does not count Alice as his sister. 3. Therefore, the number of sisters each brother has is \( M \). ### Method 4: Generalization 1. Let the total number of children be \( M + N + 1 \) (Alice included). 2. Each brother has \( M + 1 \) girls in the family (including Alice). 3. Excluding Alice, each brother has \( M \) sisters. ### Method 5: Visual Representation 1. Draw a family tree with one mother and one father. 2. Add \( M + 1 \) daughters (including Alice) and \( N \) sons. 3. Observe that each son has \( M \) sisters since Alice is also counted as a sister. ### Summary of Methods - **Method 1:** Each brother has \( M \) sisters. - **Method 2:** Each brother has \( M \) sisters. - **Method 3:** Each brother has \( M \) sisters. - **Method 4:** Each brother has \( M \) sisters. - **Method 5:** Each brother has \( M \) sisters. ### Conclusion Since all methods conclude that each of Alice’s brothers has \( M \) sisters, the final answer with the highest frequency is: **Each brother has \( M \) sisters.**
Qwen2-72B-Instruct
Method 1: Direct Logic Alice has M sisters and N brothers. When we consider Alice's brother, he shares the same family, so he also has M sisters (excluding Alice) and N-1 brothers (excluding himself). Final Answer: M sisters Method 2: Family Tree Visualization Imagine drawing a family tree. Alice is in the middle, with M branches going up to her sisters and N branches going down to her brothers. When we look at one of Alice's brothers, we can see that he has M branches going up to his sisters (excluding Alice) and N-1 branches going down to his brothers (excluding himself). Final Answer: M sisters Method 3: Algebraic Expression Let's use algebra to represent the situation. Let S be the number of sisters and B be the number of brothers (excluding Alice). We know that Alice has M sisters and N brothers. So, S = M and B = N. Now, let's consider Alice's brother. He has S sisters and B brothers. Since Alice is not counted as a sister for her brother, we have S = M and B = N-1. Final Answer: M sisters Method 4: Counterexample Let's use a counterexample to verify our answer. Suppose Alice has 2 sisters and 3 brothers. When we consider Alice's brother, he should have 2 sisters (excluding Alice) and 2 brothers (excluding himself). In this case, the number of sisters is the same as the number of sisters Alice has, which is 2. Final Answer: M sisters Method 5: Process of Elimination Let's consider other possible answers and eliminate them. The answer cannot be M+1 sisters because Alice's brother does not count Alice as his sister. The answer cannot be M-1 sisters because Alice's brother has the same number of sisters as Alice, excluding Alice herself. The answer cannot be N sisters because N represents the number of brothers Alice has, not the number of sisters her brother has. By process of elimination, the answer must be M sisters. Final Answer: M sisters Since all five methods lead to the same answer, the final answer is: M sisters
Qwen1.5-110B-Chat
Method 1: If Alice has M sisters and N brothers, then her brother has M sisters as well since they share the same set of sisters. Method 2: Considering the family structure, each of Alice's brothers would have the same number of sisters as Alice herself, because siblings share the same set of parents. Therefore, Alice's brother has M sisters. Method 3: Let's denote Alice's siblings as follows: M sisters (S) and N brothers (B), including Alice. The total number of siblings Alice's brother has is M + (N - 1) since we subtract Alice from the total brothers count to only consider siblings other than herself. However, to find out just the sisters, we only consider M, as that's the count of sisters. Method 4: If we think in terms of relationships, Alice's brother's sisters would include all of Alice's sisters but not Alice herself. Since the question is about sisters specifically, and Alice's brother shares all sisters with Alice, the number is M. Method 5: By process of elimination or direct information, the question doesn't suggest any difference in the number of sisters between Alice and her brother regarding their siblings. Thus, Alice's brother has M sisters by default, as there's no information to suggest he has a different number. Final Answer: Based on the consistency across all methods, Alice's brother has M sisters, which is the answer with the highest frequency in these lines of thinking.
Claude-3-opus-2024-0229
Great! Let's explore five different thinking methods to determine how many sisters Alice's brother has. We'll then compare the answers and choose the one with the highest frequency as the final answer. Method 1: Alice has M sisters, and each of her brothers would have the same number of sisters. Therefore, Alice's brother has M sisters. Method 2: Alice has N brothers, which means she has N+1 siblings in total (including herself). Since Alice is a sister to her brothers, each of her brothers would have (N+1)-1 = N sisters, which is the total number of siblings minus themselves. Method 3: Let's consider the total number of children in the family. There are M sisters (including Alice) and N brothers, so the total number of children is M+N. From the perspective of one of Alice's brothers, he would have (M+N)-1 siblings, and among them, M would be sisters. Method 4: We can also think about it this way: If Alice has M sisters, then each of her brothers would also have M sisters because they are all part of the same family. Method 5: Imagine you are one of Alice's brothers. You would have the same number of sisters as Alice, which is M, because you are siblings from the same family. Comparing the answers: - Method 1: M sisters - Method 2: N sisters - Method 3: M sisters - Method 4: M sisters - Method 5: M sisters The answer with the highest frequency is M sisters, appearing in four out of the five methods. Therefore, the final answer is that Alice's brother has M sisters.
Gemini-1.5-pro-api-0514
Here are five ways to think about this problem: **Method 1: Specific Example** * Imagine Alice has 2 sisters and 3 brothers. * Since they are all siblings, each brother also has those same 2 sisters. **Method 2: Focusing on the Siblings** * Alice's brothers share all of *her* sisters. * Therefore, each brother has the same number of sisters as Alice, which is M. **Method 3: Visual Representation** * Draw a circle to represent the family. * Write "Alice" inside. * Add "M sisters" on one side of Alice. * Add "N brothers" on the other side of Alice. * Each brother is in the "N brothers" group and can see the "M sisters" group. **Method 4: Eliminating Alice** * Alice is a sister to her brothers, but we want to know how many *other* sisters they have. * Since Alice is one of the M sisters, her brothers have M - 1 sisters. **Method 5: Considering Gender** * The number of brothers Alice has doesn't affect how many sisters her brothers have. * Each brother will have all the sisters in the family, which is M. **Final Answer** The most common answer among these methods is **M**. While Method 4 raises a valid point about excluding Alice when counting from the perspective of her brothers, the problem is likely asking for the total number of sisters each brother has, which includes Alice.
Yi-large-preview
To determine how many sisters Alice's brother has, let's explore five different thinking methods: ### Method 1: Direct Interpretation If Alice has M sisters, then each of her brothers also has M sisters. This is because all siblings share the same pool of sisters. ### Method 2: Counting Siblings Alice has M sisters and N brothers, making the total number of siblings M + N. Since Alice is also part of this count, we subtract 1 to exclude her from the count of her brother's sisters: M + N - 1. However, we are only interested in the sisters, so the number of sisters Alice's brother has is M. ### Method 3: Alice's Perspective From Alice's perspective, she has M sisters. Since her brothers are in the same sibling group, they would each have the same number of sisters as Alice does, which is M. ### Method 4: One Brother's Perspective Imagine we pick any one of Alice's brothers. From his perspective, he has Alice as a sister, and he has all of Alice's sisters as his sisters too. This totals to M sisters. ### Method 5: Using a Specific Example Let's say M = 3 and N = 2. Alice has 3 sisters and 2 brothers. If we list out all the siblings, we might have Alice (A), her 3 sisters (S1, S2, S3), and her 2 brothers (B1, B2). If we count the sisters from any brother's perspective, say B1, he would have S1, S2, and S3 as sisters, which is 3 sisters, matching M. ### Conclusion In all five methods, we arrive at the same answer: Alice’s brother has M sisters. This answer has the highest frequency (it appears in all methods) and is thus the correct and final answer.
DeepSeek-V2 Chat
To determine how many sisters Alice's brother has, we need to consider the relationships between Alice, her sisters, and her brothers. Here are five different thinking methods to approach this problem: 1. **Direct Counting**: If Alice has M sisters, then each of her brothers also has M sisters because they share the same sisters. This is because the sisters of Alice are also sisters to her brothers. 2. **Family Structure Analysis**: Assuming each sibling is unique (i.e., no twins), the total number of sisters is independent of whether we are considering Alice or her brothers. Therefore, if Alice has M sisters, her brothers also have M sisters. 3. **Symmetry Argument**: The family structure is symmetric with respect to Alice and her brothers regarding the number of sisters. Since the sisters are shared among all siblings, the number of sisters for Alice's brother is the same as the number of sisters for Alice. 4. **Recursive Reasoning**: If we consider the family as a whole, the number of sisters is a fixed value that does not change based on who is being considered (Alice or her brothers). Thus, Alice's brother has M sisters. 5. **Logical Deduction**: Since the question does not specify any differences in the family structure that would affect the number of sisters each brother has, we can logically deduce that Alice's brother has the same number of sisters as Alice, which is M. All five methods lead to the same conclusion: Alice's brother has M sisters. Since all methods agree, the final answer is **M**, and this answer has the highest frequency across all methods.
glm-4-0520
To determine how many sisters Alice's brother has, we must consider the perspective of one of Alice's brothers. Here are five different ways of thinking about the problem: Direct Count Method: If Alice has M sisters, then her brothers will also have the same M sisters. Alice herself does not count as one of her brother's sisters. Therefore, Alice's brother has M sisters. Inclusion-Exclusion Principle: If we include Alice in the count, there are M+1 females (Alice + her M sisters). However, since we are looking for the number of sisters from the perspective of one of her brothers, we subtract 1 for Alice. Thus, the number of sisters Alice's brother has is M+1-1 = M. Family Composition Approach: Each child in the family has the same set of siblings. Therefore, the number of sisters for each brother is the same as the number of sisters for Alice. So, Alice's brother has M sisters. Role Reversal Method: If we reverse the roles, we ask how many brothers Alice's sister has. We know that Alice has N brothers, so her sister would have N brothers. Since the question is symmetric in terms of brothers and sisters, Alice's brother would have the same number of sisters as Alice's sister has brothers, which is M. Siblings’ Perspective Method: Each of Alice's brothers considers Alice as a sister. However, when considering how many sisters one of the brothers has, we need to exclude Alice herself from that count. Therefore, the number of sisters each brother has is M (excluding Alice). Consensus and Conclusion: All five methods yield the same answer: Alice's brother has M sisters. The answer with the highest frequency is M, as it is the result given by all five methods.
im-a-good-gpt2-chatbot
To determine how many sisters Alice's brother has, let’s explore different ways of thinking about the problem. ### Method 1: Direct Counting Alice has \( M \) sisters and \( N \) brothers. Each of Alice's brothers would have the same number of sisters as Alice herself, because all the siblings share the same family members. - Alice has \( M \) sisters. - But, Alice's brothers would also count Alice as a sister. - Therefore, each brother has \( M + 1 \) sisters (the \( M \) sisters plus Alice herself). ### Method 2: Sibling Perspective Consider the perspective of one of Alice's brothers: - He would count all of Alice’s \( M \) sisters as his sisters. - He would also count Alice as an additional sister. - Thus, he has \( M + 1 \) sisters. ### Method 3: Family Tree Analysis Look at the family structure: - The total number of children is \( M + N + 1 \) (including Alice). - The number of girls (sisters plus Alice) is \( M + 1 \). - Since we’re looking for the number of sisters from a brother’s point of view, he counts all the girls except himself, which is \( M + 1 \). ### Method 4: Algebraic Approach Let \( s \) be the number of sisters a brother has. - Alice has \( M \) sisters, so a brother has those \( M \) sisters plus Alice. - \( s = M + 1 \). ### Method 5: Logical Reasoning By definition: - A brother will count all female siblings as sisters. - There are \( M \) other girls and Alice, - So, \( M + 1 \) sisters for each brother. ### Conclusion All methods (Direct Counting, Sibling Perspective, Family Tree Analysis, Algebraic Approach, and Logical Reasoning) lead to the same answer: \[ \boxed{M + 1} \] This consistency across different approaches confirms that the answer is robust and reliable. The final answer, with the highest frequency from our analysis, is \( \boxed{M+1} \).
In this section, I use Self-Consistency to test the model. I've found that most models lean towards the belief that Alice should not be considered a sister from her brother's perspective, failing to answer correctly. However, the model im-a-good-gpt2-chatbot is an exception. It correctly answers the question using five different methods.
3-Conclusion and Limitation
I've tested many of the main models currently on the market, discovering that most struggle to correctly answer the Alice Question and its variations. Despite their ability to perform reasoning, these models often err during the reasoning process. Techniques like CoT and few-shot remain useful, as do classic prompting methods.
However, this test has some limitations. For one, I didn't repeat the questions multiple times, which might have mitigated potential model instability. Additionally, other prompting techniques that I didn't test could potentially answer the question correctly. Lastly, although the LLM is a powerful tool, this question does not necessarily showcase its capabilities, even if it had difficulty providing a correct answer.