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Reasoning

Reasoning is the next step of CoT (Chain of Thought), naturally used to describe the logical steps generated by the model before reaching a conclusion. Reasoning strengthens this characteristic by going through training steps that encourage the model to generate chains of thought freely before producing the final answer. This allows models to explore the problem more profoundly and ultimately reach a better solution to the best of their ability by using extra compute time to generate more tokens and improve the answer—also described as Test Time Computation.

They excel at complex use cases like math and coding tasks, but can be used in a wide range of scenarios to solve diverse problems.

reasoning_graph

The output of reasoning models will hence be split into 2 sections, the reasoning section between the <think> and </think> tags, where you can find the reasoning traces the model generated, and the final answer outside of the <think> tags.

Currently we have two reasoning models:

  • magistral-small-2506: Our open smaller version for open research and efficient reasoning.
  • magistral-medium-2506: Our more powerful reasoning model balancing performance and cost.

To have the best performance out of our models, we recommend having the following system prompt (currently default):

System Prompt
A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown to format your response. Write both your thoughts and summary in the same language as the task posed by the user. NEVER use \boxed{} in your response.

Your thinking process must follow the template below:
<think>
Your thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.
</think>

Here, provide a concise summary that reflects your reasoning and presents a clear final answer to the user. Don't mention that this is a summary.

Problem:


With escape characters, the system prompt would look like this:

A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown to format your response. Write both your thoughts and summary in the same language as the task posed by the user. NEVER use \\boxed{} in your response.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user. Don't mention that this is a summary.\n\nProblem:\n\n

You can use our reasoning models in a similar way to how you would use our other text models, here is an example via our chat completions endpoint:

import os
from mistralai import Mistral

api_key = os.environ["MISTRAL_API_KEY"]
model = "magistral-medium-2506"

client = Mistral(api_key=api_key)

chat_response = client.chat.complete(
    model = model,
    messages = [
        {
            "role": "user",
            "content": "John is one of 4 children. The first sister is 4 years old. Next year, the second sister will be twice as old as the first sister. The third sister is two years older than the second sister. The third sister is half the age of her older brother. How old is John?",
        },
    ]
)

print(chat_response.choices[0].message.content)

The raw output of the model will include a long string with the entire chain of thought generated encapsulated between the thinking tags, usually in the following format:

<think>\n*thoughts and reasoning traces will go here*\n</think>\n*final answer will go here*
Raw Output
<think>\nOkay, let's tackle this problem step by step. We have information about John and his three sisters. Let's list out what we know and try to derive each person's age.\n\n1. **First Sister**: The first sister is 4 years old. That's straightforward.\n\n   - First sister's age = 4 years\n\n2. **Second Sister**: Next year, the second sister will be twice as old as the first sister.\n\n   - First sister's age next year = 4 + 1 = 5 years\n   - So, second sister's age next year = 2 * 5 = 10 years\n   - Therefore, second sister's current age = 10 - 1 = 9 years\n\n3. **Third Sister**: The third sister is two years older than the second sister.\n\n   - Second sister's current age = 9 years\n   - So, third sister's age = 9 + 2 = 11 years\n\n4. **John (the older brother)**: The third sister is half the age of her older brother.\n\n   - Third sister's age = 11 years\n   - So, older brother's age = 11 * 2 = 22 years\n   - Therefore, John's age = 22 years\n\nBut wait, let's double-check this because the problem states that John is one of 4 children. That means there are four children in total: John and his three sisters. So, if John is the older brother, then the third sister is 11, and John is 22. But let's verify all the steps to ensure no mistakes were made.\n\n- First sister: 4 years old\n- Next year, first sister will be 5 years old\n- Next year, second sister will be twice as old as the first sister, so 2 * 5 = 10 years old next year\n- Therefore, second sister's current age is 10 - 1 = 9 years old\n- Third sister is two years older than the second sister: 9 + 2 = 11 years old\n- Third sister is half the age of her older brother: so older brother is 11 * 2 = 22 years old\n\nBut wait, if John is one of 4 children, and we have three sisters and John, that makes sense. The ages are:\n- First sister: 4\n- Second sister: 9\n- Third sister: 11\n- John: 22\n\nLet me check if all conditions are satisfied:\n\n1. First sister is 4 years old. ✔️\n2. Next year, first sister will be 5, and second sister will be 10, which is twice 5. ✔️\n3. Third sister is 11, which is 2 years older than the second sister (9 + 2 = 11). ✔️\n4. Third sister is half the age of her older brother. So older brother is 22, and half of that is 11, which matches the third sister's age. ✔️\n\nEverything checks out!\n\nBut wait, the problem says \"John is one of 4 children.\" That could mean that there are 4 children in total, including John. But in our count, we have three sisters and John, which is 4 children. So our initial assumption seems correct.\n\nBut let's think again: if John is one of 4 children, that means there are 3 other children besides John. So the three sisters and John would be 4 children. So our count seems correct.\n\nBut let's think about the wording: \"The third sister is half the age of her older brother.\" If John is the older brother, then that would mean John is older than the third sister. In our calculation, John is 22, and the third sister is 11, which fits because 11 is half of 22.\n\nBut just to be sure, let's consider if there's another older brother. The problem says \"the third sister is half the age of her older brother.\" It doesn't specify that John is the older brother, but since John is one of the 4 children, and we have three sisters, it's possible that John is the older brother.\n\nBut if there were another brother, then we'd have more than 4 children (three sisters, John, and another brother), which contradicts the given information that John is one of 4 children. So, John must be the older brother.\n\nTherefore, John's age is 22 years.\n\nWait a minute, let me re-examine the problem statement: \"John is one of 4 children. The first sister is 4 years old. Next year, the second sister will be twice as old as the first sister. The third sister is two years older than the second sister. The third sister is half the ago of her older brother. How old is John?\"\n\nOkay, so we have:\n\n1. Total children: 4 (John and 3 sisters)\n2. First sister: 4 years old\n3. Next year, second sister's age = 2 * (first sister's age next year)\n   - First sister next year: 4 + 1 = 5\n   - So, second sister next year: 2 * 5 = 10\n   - Therefore, second sister now: 10 - 1 = 9\n4. Third sister is two years older than the second sister: 9 + 2 = 11\n5. Third sister is half the age of her older brother: so older brother's age = 2 * 11 = 22\n\nNow, who is the older brother? The children are: John and three sisters. So the older brother must be John, unless there's another brother, but since there are only 4 children and three are sisters, John must be the brother.\n\nBut wait, the problem says \"the third sister is half the age of her older brother.\" If John is the brother, then he is the older brother, and his age is 22.\n\nBut let's think about the order of the sisters. The first sister is 4, second is 9, third is 11. So the ages are 4, 9, 11 for the sisters, and John is 22. That seems consistent because 22 is older than 11 (the third sister).\n\nBut let's check if there could be another brother. The problem says \"John is one of 4 children,\" and we have three sisters, so the fourth child must be John. Therefore, John is the only brother, and he is the older brother referred to in the problem.\n\nTherefore, John is 22 years old.\n\nBut wait, let's think about the phrasing: \"the third sister is half the age of her older brother.\" This implies that the older brother is not necessarily John. Maybe there's another brother older than John, making John not the oldest. But the problem states that John is one of 4 children, meaning the siblings are: three sisters and John, totaling 4 children. Therefore, there cannot be another brother; John must be the only brother and thus the older brother referred to.\n\nWait, but the problem says \"her older brother,\" implying that the older brother is someone other than the third sister. But since there are only four children: three sisters and John, and the third sister has an older brother, that older brother must be John.\n\nBut if John is the older brother, and the third sister is 11, then John would be 22. But is John necessarily the oldest? Could there be another brother older than John? No, because there are only four children: three sisters and John. So John must be the older brother.\n\nWait, no, the problem says \"the third sister is half the age of her older brother.\" It doesn't say that John is the older brother; it just says that John is one of the four children. So the four children are: three sisters and John. And the third sister has an older brother, which must be John, because there are no other brothers. So John must be the older brother, making him 22.\n\nBut let me think again: the four children are: first sister, second sister, third sister, and John. The third sister has an older brother. Among the four children, the possible older brothers would be... well, the sisters are all girls, so the only possible brother is John. Therefore, John must be the older brother, and his age is 22.\n\nBut wait, could one of the sisters be older than John? The problem doesn't specify the order of ages among the siblings, only that the third sister has an older brother. But since all the other siblings are sisters (three sisters and John), the older brother must be John.\n\nWait, no, the siblings are: first sister, second sister, third sister, and John. The third sister is 11. Her older brother would have to be older than 11. The other sisters are 4 and 9, so they are younger. Therefore, the older brother must be John, and his age is 22.\n\nBut let me think if there's another interpretation. Maybe \"the third sister is half the age of her older brother\" implies that the older brother is not necessarily John. But since there are only four children (three sisters and John), the older brother must be John.\n\nWait, unless one of the sisters is older than John, but then that sister would be the older sister, not brother. So the older brother must be John.\n\nTherefore, John is 22 years old.\n\nBut let me think again about the siblings' ages to ensure consistency:\n\n- First sister: 4\n- Second sister: 9\n- Third sister: 11\n- John: ?\n\nFrom the problem: \"The third sister is half the age of her older brother.\" So older brother's age = 2 * third sister's age = 2 * 11 = 22. So John is 22.\n\nBut let's see the order of ages: 4, 9, 11, and 22. That seems consistent because 22 is older than 11, so John is indeed the older brother.\n\nWait a minute, but the first sister is 4, second is 9, third is 11, and John is 22. That would mean the order from youngest to oldest is: first sister (4), second sister (9), third sister (11), and John (22). That makes sense because each subsequent sibling is older than the previous one, and John is the oldest.\n\nTherefore, John is 22 years old.\n\nBut before finalizing, let me check if there's another way to interpret the problem. Maybe the order of the sisters is not by age but just by mention. The problem says \"the first sister,\" not necessarily the youngest. But usually, when we say first, second, third, it's in order of age, with first being the youngest, but that's not necessarily the case. However, in age problems, it's common to list siblings in order of age, but the problem doesn't specify.\n\nBut the problem says \"the first sister is 4 years old,\" and then talks about the second and third sisters, implying that first, second, third refer to their order in the family, not necessarily by age. But usually, first, second, third would refer to birth order, meaning first is the oldest, but that contradicts the ages we have because the first sister is 4, which would be the youngest.\n\nWait, in English, when we say \"first sister,\" \"second sister,\" etc., it typically refers to the order of birth, with first being the oldest. But in this case, the first sister is 4 years old, which is younger than the second sister (9) and third sister (11). So \"first,\" \"second,\" \"third\" here must refer to some other order, not birth order.\n\nBut in common usage, first, second, third sister would refer to birth order, with first being the oldest. If that's the case, then:\n\n- First sister (oldest sister): 4 years old\n- Second sister: ?\n- Third sister: ?\nBut then the first sister being the oldest at 4 doesn't make sense because the other sisters would have to be younger, but the second sister is 9 next year which would make her older than 4 now, which contradicts the first sister being the oldest.\n\nTherefore, \"first,\" \"second,\" \"third\" must not refer to birth order but perhaps the order in which they are mentioned or some other order. For the sake of the problem, it's likely that \"first,\" \"second,\" \"third\" are just labels and not indicative of birth order, because if first sister is 4 and second is older (9), that's not possible if first is the oldest.\n\nSo let's assume that \"first,\" \"second,\" \"third\" are just labels and not indicative of birth order.\n\nThen we have:\n\n- Sister A (first sister): 4\n- Sister B (second sister): current age is 9 (since next year she'll be 10)\n- Sister C (third sister): 11\n- John: ?\n\nFrom the problem: \"The third sister is half the age of her older brother.\" So older brother's age is 22, hence John is 22.\n\nBut is John necessarily the older brother? There are four children: three sisters and John. So the siblings are: Sister A (4), Sister B (9), Sister C (11), and John.\n\nFor Sister C (11) to have an older brother, that brother must be older than 11. The other siblings are 4, 9, and John. So John must be older than 11 to be the older brother. So John is 22, which is older than 11, so that checks out.\n\nBut wait, could one of the sisters be older than John? The sisters are 4, 9, and 11. So none of the sisters are older than John if John is 22.\n\nBut is John necessarily the older brother? The problem says John is one of the four children, and the four children are three sisters and John. So the older brother must be John, because the other siblings are sisters.\n\nTherefore, John is the older brother, and his age is 22.\n\nBut let me think if there's any ambiguity. The problem says \"the third sister is half the age of her older brother.\" It doesn't specify that the older brother is John; it just says \"her older brother.\" But among the four children (three sisters and John), the only possible older brother is John, because the other siblings are sisters. So John must be the older brother, making him 22.\n\nBut let me think if there's any other possibility. Could \"her older brother\" refer to someone outside the four children? No, because the four children consist of John and his three sisters, so the older brother must be within these four, which is John.\n\nTherefore, John is 22 years old.\n\nBut let me think one more time to ensure no mistakes. Let's list the siblings and their ages:\n\n1. First sister: 4 years old\n2. Second sister: currently 9 (since next year she'll be 10, which is twice the first sister's age next year, which is 5)\n3. Third sister: 11 (which is 2 years older than the second sister's current age of 9)\n4. John: ?\n\nThe third sister is half the age of her older brother. So older brother's age = 2 * 11 = 22. Therefore, John is 22.\n\nNow, is John indeed the older brother? Let's see the ages: 4, 9, 11, and 22. So the order from youngest to oldest is: 4, 9, 11, 22. So John at 22 is the oldest, hence the older brother to the third sister (11).\n\nTherefore, John is 22 years old.\n\nBut wait, the problem says \"John is one of 4 children.\" So the four children are: first sister (4), second sister (9), third sister (11), and John (22). That adds up to four children, and John is indeed the older brother to the third sister.\n\nBut let me think if there's another way to interpret the problem. Maybe \"the first sister is 4 years old\" doesn't necessarily mean she's the youngest. Maybe the sisters are ordered differently. But the problem lists them as first, second, third, which typically implies birth order where first is the oldest. But if first sister is 4, and second is older (since next year she's twice as old as first sister next year), that contradicts first being the oldest.\n\nWait, let's assume \"first,\" \"second,\" \"third\" refer to birth order, where first is the oldest.\n\nThen:\n\n- First sister (oldest): 4\nBut then the second sister is younger than the first, but next year the second sister will be twice as old as the first sister next year.\n\nLet’s try this interpretation.\n\n1. First sister (oldest): 4 years old\n2. Next year:\n   - First sister: 4 + 1 = 5\n   - Second sister will be twice as old as first sister next year: so second sister next year will be 2 * 5 = 10, so current age is 10 - 1 = 9\nBut if first sister is oldest at 4, second sister is younger, so should be less than 4, but we got 9, which is older than 4. This contradicts the assumption that first sister is the oldest.\n\nTherefore, \"first,\" \"second,\" \"third\" cannot refer to birth order where first is oldest. Maybe \"first,\" \"second,\" \"third\" are just labels not indicating age order.\n\nSo let's stick with the initial interpretation where \"first,\" \"second,\" \"third\" are just labels, not indicating birth order, and we have:\n\n- First sister: 4\n- Second sister: currently 9 (since next year she'll be 10, which is twice the first sister's age next year, which is 5)\n- Third sister: 11 (which is 2 years older than the second sister's current age of 9)\n- John: ?\n\nThird sister is half the age of her older brother, so older brother is 22, hence John is 22.\n\nThis seems consistent. Let me list the siblings and their ages:\n\n1. First sister: 4\n2. Second sister: 9\n3. Third sister: 11\n4. John: 22\n\nNow, let's check the birth order based on ages. The order from youngest to oldest would be: 4 (first sister), 9 (second sister), 11 (third sister), 22 (John).\n\nSo in terms of birth order (assuming older siblings are born first), the order would be:\n\n1. John: 22 (oldest)\n2. Third sister: 11\n3. Second sister: 9\n4. First sister: 4 (youngest)\n\nBut the problem refers to them as first, second, third sisters, not in birth order but perhaps in some other order (maybe order of mention in the problem).\n\nGiven that, and since John is the oldest (22), then the third sister (11) has an older brother, which is John, satisfying the condition.\n\nTherefore, John is 22 years old.\n\n</think>\n\nJohn is 22 years old.\n\nHere's the summary:\n\nWe are given that John is one of four children, with three sisters. The first sister is 4 years old. Next year, the second sister will be twice as old as the first sister will be next year (which is 5), making the second sister currently 9 years old. The third sister is two years older than the second sister, so she is 11 years old. The third sister is half the age of her older brother, which means the older brother is 22 years old. Since John is the only brother among the four children (three sisters and John), he must be the older brother, making John 22 years old.\n\nTherefore, John is 22 years old.",

We can see that the model is able to reason through the problem and arrive at the correct answer, let's format each section in markdown:

Rendered Thinking

Okay, let's tackle this problem step by step. We have information about John and his three sisters. Let's list out what we know and try to derive each person's age.

  1. First Sister: The first sister is 4 years old. That's straightforward.

    • First sister's age = 4 years

  2. Second Sister: Next year, the second sister will be twice as old as the first sister.

    • First sister's age next year = 4 + 1 = 5 years
    • So, second sister's age next year = 2 * 5 = 10 years
    • Therefore, second sister's current age = 10 - 1 = 9 years

  3. Third Sister: The third sister is two years older than the second sister.

    • Second sister's current age = 9 years
    • So, third sister's age = 9 + 2 = 11 years

  4. John (the older brother): The third sister is half the age of her older brother.

    • Third sister's age = 11 years
    • So, older brother's age = 11 * 2 = 22 years
    • Therefore, John's age = 22 years

But wait, let's double-check this because the problem states that John is one of 4 children. That means there are four children in total: John and his three sisters. So, if John is the older brother, then the third sister is 11, and John is 22. But let's verify all the steps to ensure no mistakes were made.

  • First sister: 4 years old
  • Next year, first sister will be 5 years old
  • Next year, second sister will be twice as old as the first sister, so 2 * 5 = 10 years old next year
  • Therefore, second sister's current age is 10 - 1 = 9 years old
  • Third sister is two years older than the second sister: 9 + 2 = 11 years old
  • Third sister is half the age of her older brother: so older brother is 11 * 2 = 22 years old

But wait, if John is one of 4 children, and we have three sisters and John, that makes sense. The ages are:

  • First sister: 4
  • Second sister: 9
  • Third sister: 11
  • John: 22

Let me check if all conditions are satisfied:

  1. First sister is 4 years old. ✔️
  2. Next year, first sister will be 5, and second sister will be 10, which is twice 5. ✔️
  3. Third sister is 11, which is 2 years older than the second sister (9 + 2 = 11). ✔️
  4. Third sister is half the age of her older brother. So older brother is 22, and half of that is 11, which matches the third sister's age. ✔️

Everything checks out!

But wait, the problem says "John is one of 4 children." That could mean that there are 4 children in total, including John. But in our count, we have three sisters and John, which is 4 children. So our initial assumption seems correct.

But let's think again: if John is one of 4 children, that means there are 3 other children besides John. So the three sisters and John would be 4 children. So our count seems correct.

But let's think about the wording: "The third sister is half the age of her older brother." If John is the older brother, then that would mean John is older than the third sister. In our calculation, John is 22, and the third sister is 11, which fits because 11 is half of 22.

But just to be sure, let's consider if there's another older brother. The problem says "the third sister is half the age of her older brother." It doesn't specify that John is the older brother; it just says that John is one of the four children. So the four children are: three sisters and John. And the third sister has an older brother, which must be John, because there are no other brothers. So John must be the older brother, making him 22.

But if there were another brother, then we'd have more than 4 children (three sisters, John, and another brother), which contradicts the given information that John is one of 4 children. So, John must be the older brother.

Therefore, John's age is 22 years.

Wait a minute, let me re-examine the problem statement: "John is one of 4 children. The first sister is 4 years old. Next year, the second sister will be twice as old as the first sister. The third sister is two years older than the second sister. The third sister is half the ago of her older brother. How old is John?"

Okay, so we have:

  1. Total children: 4 (John and 3 sisters)
  2. First sister: 4 years old
  3. Next year, second sister's age = 2 * (first sister's age next year)
    • First sister next year: 4 + 1 = 5
    • So, second sister next year: 2 * 5 = 10
    • Therefore, second sister now: 10 - 1 = 9
  4. Third sister is two years older than the second sister: 9 + 2 = 11
  5. Third sister is half the age of her older brother: so older brother's age = 2 * 11 = 22

Now, who is the older brother? The children are: John and three sisters. So the older brother must be John, unless there's another brother, but since there are only 4 children and three are sisters, John must be the brother.

But wait, the problem says "the third sister is half the age of her older brother." If John is the brother, then he is the older brother, and his age is 22.

But let's think about the order of the sisters. The first sister is 4, second is 9, third is 11. So the ages are 4, 9, 11 for the sisters, and John is 22. That seems consistent because 22 is older than 11 (the third sister).

But let's check if there could be another brother. The problem says "John is one of 4 children," and we have three sisters, so the fourth child must be John. Therefore, John is the only brother, and he is the older brother referred to in the problem.

Therefore, John is 22 years old.

But wait, let's think about the phrasing: "the third sister is half the age of her older brother." This implies that the older brother is not necessarily John. Maybe there's another brother older than John, making John not the oldest. But the problem states that John is one of 4 children, meaning the siblings are: three sisters and John, totaling 4 children. Therefore, there cannot be another brother; John must be the only brother and thus the older brother referred to.

Wait, but the problem says "her older brother," implying that the older brother is someone other than the third sister. But since there are only four children: three sisters and John, and the third sister has an older brother, that older brother must be John.

But if John is the older brother, and the third sister is 11, then John would be 22. But is John necessarily the oldest? Could there be another brother older than John? No, because there are only four children: three sisters and John. So John must be the older brother.

Wait, no, the problem says "the third sister is half the age of her older brother." It doesn't say that John is the older brother; it just says that John is one of the four children. So the four children are: three sisters and John. And the third sister has an older brother, which must be John, because there are no other brothers. So John must be the older brother, making him 22.

But just to be sure, let's consider if there's another interpretation. Maybe "the first sister is 4 years old" doesn't necessarily mean she's the youngest. Maybe the sisters are ordered differently. But the problem lists them as first, second, third, which typically implies birth order, with first being the oldest. But in this case, the first sister is 4, which is younger than the second sister (9) and third sister (11). So "first," "second," "third" here must refer to some other order, not birth order.

But in common usage, first, second, third sister would refer to birth order, with first being the oldest. If that's the case, then:

  • First sister (oldest sister): 4 years old
  • Second sister: ?
  • Third sister: ?

But then the first sister being the oldest at 4 doesn't make sense because the other sisters would have to be younger, but the second sister is 9 next year which would make her older than 4 now, which contradicts the first sister being the oldest.

Therefore, "first," "second," "third" must not refer to birth order but perhaps the order in which they are mentioned or some other order. For the sake of the problem, it's likely that "first," "second," "third" are just labels and not indicative of birth order, because if first sister is 4 and second is older (9), that's not possible if first is the oldest.

So let's assume that "first," "second," "third" are just labels and not indicative of birth order.

Then we have:

  • Sister A (first sister): 4
  • Sister B (second sister): current age is 9 (since next year she'll be 10)
  • Sister C (third sister): 11
  • John: ?

From the problem: "The third sister is half the age of her older brother." So older brother's age is 22, hence John is 22.

But is John necessarily the older brother? There are four children: three sisters and John. So the siblings are: Sister A (4), Sister B (9), Sister C (11), and John.

For Sister C (11) to have an older brother, that brother must be older than 11. The other siblings are 4, 9, and John. So John must be older than 11 to be the older brother. So John is 22, which is older than 11, so that checks out.

But wait, could one of the sisters be older than John? The sisters are 4, 9, and 11. So none of the sisters are older than John if John is 22.

But is John necessarily the older brother? The problem says John is one of the four children, and the four children are three sisters and John. So the older brother must be John, because the other siblings are sisters.

Therefore, John is the older brother, and his age is 22.

But let me think if there's any ambiguity. The problem says "the third sister is half the age of her older brother." It doesn't specify that the older brother is John; it just says "her older brother." But among the four children (three sisters and John), the only possible older brother is John, because the other siblings are sisters. So John must be the older brother, making him 22.

But let me think if there's any other possibility. Could "her older brother" refer to someone outside the four children? No, because the four children consist of John and his three sisters, so the older brother must be within these four, which is John.

Therefore, John is 22 years old.

But let me think one more time to ensure no mistakes. Let's list the siblings and their ages:

  1. First sister: 4 years old
  2. Second sister: currently 9 (since next year she'll be 10, which is twice the first sister's age next year, which is 5)
  3. Third sister: 11 (which is 2 years older than the second sister's current age of 9)
  4. John: ?

The third sister is half the age of her older brother. So older brother's age = 2 * 11 = 22. Therefore, John is 22.

Now, is John indeed the older brother? Let's see the ages: 4, 9, 11, and 22. So the order from youngest to oldest is: 4, 9, 11, 22. So John at 22 is the oldest, hence the older brother to the third sister (11).

Therefore, John is 22 years old.

But wait, the problem says "John is one of 4 children." So the four children are: first sister (4), second sister (9), third sister (11), and John (22). That adds up to four children, and John is indeed the older brother to the third sister.

But let me think if there's another way to interpret the problem. Maybe "the first sister is 4 years old" doesn't necessarily mean she's the youngest. Maybe the sisters are ordered differently. But the problem lists them as first, second, third, which typically implies birth order where first is the oldest. But if first sister is 4, and second is older (since next year she's twice as old as first sister next year), that contradicts first being the oldest.

Wait, let's assume "first," "second," "third" refer to birth order, where first is the oldest.

Then:

  • First sister (oldest): 4 But then the second sister is younger than the first, but next year she's twice as old as first sister next year.

Let’s try this interpretation.

  1. First sister (oldest): 4 years old
  2. Next year:
    • First sister: 4 + 1 = 5
    • Second sister will be twice as old as first sister next year: so second sister next year will be 2 * 5 = 10, so current age is 10 - 1 = 9 But if first sister is oldest at 4, second sister is younger, so should be less than 4, but we got 9, which is older than 4. This contradicts the assumption that first is the oldest.

Therefore, "first," "second," "third" cannot refer to birth order where first is oldest. Maybe "first," "second," "third" are just labels not indicating age order.

So let's stick with the initial interpretation where "first," "second," "third" are just labels, not indicating birth order, and we have:

  • First sister: 4
  • Second sister: currently 9 (since next year she'll be 10, which is twice the first sister's age next year, which is 5)
  • Third sister: 11 (which is 2 years older than the second sister's current age of 9)
  • John: ?

Third sister is half the age of her older brother, so older brother is 22, hence John is 22.

This seems consistent. Let me list the siblings and their ages:

  1. First sister: 4
  2. Second sister: 9
  3. Third sister: 11
  4. John: 22

Now, let's check the birth order based on ages. The order from youngest to oldest would be: 4 (first sister), 9 (second sister), 11 (third sister), 22 (John).

So in terms of birth order (assuming older siblings are born first), the order would be:

  1. John: 22 (oldest)
  2. Third sister: 11
  3. Second sister: 9
  4. First sister: 4 (youngest)

But the problem refers to them as first, second, third sisters, not in birth order but perhaps in some other order (maybe order of mention in the problem).

Given that, and since John is the oldest (22), then the third sister (11) has an older brother, which is John, satisfying the condition.

Therefore, John is 22 years old.

Rendered Answer

John is 22 years old.

Here's the summary:

We are given that John is one of four children, with three sisters. The first sister is 4 years old. Next year, the second sister will be twice as old as the first sister will be next year (which is 5), making the second sister currently 9 years old. The third sister is two years older than the second sister, so she is 11 years old. The third sister is half the age of her older brother, which means the older brother is 22 years old. Since John is the only brother among the four children (three sisters and John), he must be the older brother, making John 22 years old.

Therefore, John is 22 years old.