1[
2  {
3    "role": "system",
4    "content": [
5      {
6        "type": "text",
7        "text": "System prompt, with both instructions and"
8      },
9      {
10        "type": "thinking",
11        "thinking": [
12          {
13            "type": "text",
14            "text": "Encapsulated reasoning instructions."
15          }
16        ]
17      }
18    ]
19  },
20  {
21    "role": "user",
22    "content": [
23      {
24        "type": "text",
25        "text": "User input."
26      }
27    ]
28  },
29  {
30    "role": "assistant",
31    "content": [
32      {
33        "type": "thinking",
34        "thinking": [
35          {
36            "type": "text",
37            "text": "Reasoning traces."
38          }
39        ]
40      },
41      {
42        "type": "text",
43        "text": "Followed by the final answer."
44      }
45    ]
46  }
47]

1import os
2from mistralai import Mistral
3
4api_key = os.environ["MISTRAL_API_KEY"]
5model = "magistral-medium-latest"
6
7client = Mistral(api_key=api_key)
8
9chat_response = client.chat.complete(
10    model = model,
11    messages = [
12        {
13            "role": "user",
14            "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?",
15        },
16    ],
17    # prompt_mode = "reasoning" if you want to explicitly use the default system prompt, or None if you want to opt out of the default system prompt.
18)
19
20print(chat_response.choices[0].message.content)

1import { Mistral } from '@mistralai/mistralai';
2import * as dotenv from 'dotenv';
3
4dotenv.config();
5
6const apiKey = process.env.MISTRAL_API_KEY;
7
8const client = new Mistral({ apiKey: apiKey });
9
10async function main() {
11  const chatResponse = await client.chat.complete({
12    model: 'magistral-medium-latest',
13    messages: [
14      {
15        role: 'user',
16        content:
17          '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?',
18      },
19    ],
20    // prompt_mode: "reasoning" if you want to explicitly use the default system prompt, or null if you want to opt out of the default system prompt.
21  });
22
23  console.log('Chat:', chatResponse.choices?.[0]?.message?.content);
24}
25
26main();

1curl --location "https://api.mistral.ai/v1/chat/completions" \
2     --header 'Content-Type: application/json' \
3     --header 'Accept: application/json' \
4     --header "Authorization: Bearer $MISTRAL_API_KEY" \
5     --data '{
6    "model": "magistral-medium-latest",
7    "messages": [
8     {
9        "role": "user",
10        "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?"
11      }
12    ]
13  }'

1{
2  "model": "magistral-medium-2507",
3  "usage": {
4    "prompt_tokens": 173,
5    "total_tokens": 11170,
6    "completion_tokens": 10997
7  },
8  "object": "chat.completion",
9  "choices": [
10    {
11      "index": 0,
12      "finish_reason": "stop",
13      "message": {
14        "role": "assistant",
15        "tool_calls": null,
16        "content": [
17          {
18            "type": "thinking",
19            "thinking": [
20              {
21                "type": "text",
22                "text": "Alright, let's break this problem down systematically.\n\n1. Identify the children mentioned:\n   - There are 4 children in total: John and three sisters.\n\n2. Information about the sisters:\n   - First sister: 4 years old.\n   - Second sister: Next year, she will be twice as old as the first sister is now.\n     - Current age of first sister: 4 years.\n     - Next year, the first sister will be 5 years old.\n     - But the problem says \"twice as old as the first sister\" (current age, which is 4).\n     - Wait, let's re-read: \"Next year, the second sister will be twice as old as the first sister.\"\n       - Next year, the first sister will be 5 (since she's 4 now).\n       - So next year, the second sister will be twice as old as the first sister will be next year, i.e., twice 5 = 10 years old next year.\n       - Therefore, currently, the second sister is 10 - 1 = 9 years old.\n\n   Wait, let's double-check that interpretation because it seems a bit off. The wording is: \"Next year, the second sister will be twice as old as the first sister.\"\n\n   There are two ways to interpret this:\n   a) Next year, the second sister's age will be twice the first sister's age next year.\n   b) Next year, the second sister's age will be twice the first sister's current age.\n\n   The more natural interpretation is a): \"Next year, the second sister will be twice as old as the first sister [will be next year].\"\n\n   So:\n   - First sister's current age: 4\n   - Next year, first sister will be 5.\n   - Next year, second sister will be twice that, so 10.\n   - Therefore, second sister's current age is 10 - 1 = 9.\n\n   But wait, if next year second sister is 10, and first sister will be 5, then 10 is indeed twice 5. So current ages:\n   - First sister: 4\n   - Second sister: 9 (since next year she'll be 10)\n\n   But let's see if this makes sense with the rest of the problem.\n\n3. Third sister's age:\n   - The third sister is two years older than the second sister.\n   - Second sister is currently 9, so third sister is 9 + 2 = 11 years old.\n\n4. Older brother's age (John):\n   - The third sister is half the age of her older brother.\n   - Third sister is 11, so older brother is 11 * 2 = 22 years old.\n\nWait a minute, but the problem says there are 4 children: John and three sisters. So John is one of the four, and the other three are sisters. So if John is the older brother, then the four children are:\n1. First sister: 4\n2. Second sister: 9\n3. Third sister: 11\n4. John: ?\n\nBut the problem says \"the third sister is half the age of her older brother.\" So John is the older brother, meaning he's older than the third sister (11). So if third sister is half his age, then John is 22.\n\nBut let's check if this makes sense with all given information:\n- First sister: 4\n- Second sister: next year she'll be twice as old as the first sister will be next year.\n   - Next year, first sister: 5\n   - So second sister next year: 10, so now she's 9.\n- Third sister is two years older than second sister: 9 + 2 = 11.\n- Third sister is half as old as her older brother (John): so John is 22.\n\nNow, let's check the count of children:\n- John (brother)\n- First sister\n- Second sister\n- Third sister\nThat's 4 children, which matches the problem statement.\n\nBut wait, the problem says \"John is one of 4 children.\" So the four children are:\n1. John\n2. First sister\n3. Second sister\n4. Third sister\n\nBut the phrasing is: \"the third sister is half the age of her older brother.\" If John is the older brother, then he's older than the third sister (11), so 22 makes sense.\n\nBut let me think if there's another way to interpret it. Could \"her older brother\" refer to someone else? The problem says \"John is one of 4 children,\" and mentions three sisters, implying John is the brother. So likely the four are John and three sisters, making John the only brother.\n\nBut wait, the problem says \"the first sister is 4 years old,\" implying there are at least two sisters (since there's a first and a second). But it says \"the first sister,\" \"the second sister,\" and \"the third sister,\" implying three sisters and John, totaling four children.\n\nSo the ages are:\n- First sister: 4\n- Second sister: 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 9 + 2)\n- John: ?\n\nThe third sister is half the age of her older brother. So if the older brother is John, then John is 22.\n\nBut let's see if there's another possibility. Could there be another brother? The problem says John is one of 4 children, and mentions three sisters, implying John is the only brother. So likely John is the older brother referred to.\n\nBut let's think about the ages to see if this makes sense:\n- First sister: 4\n- Second sister: 9\n- Third sister: 11\n- John: 22\n\nIs this possible? Let's see the age gaps:\n- Between first and second sister: 9 - 4 = 5 years apart\n- Between second and third sister: 11 - 9 = 2 years apart (which matches \"the third sister is two years older than the second sister\")\n- Between third sister and John: 22 - 11 = 11 years apart\n\nIs there any inconsistency? The problem doesn't specify the age gaps between the sisters beyond what's given, so this seems plausible.\n\nBut let me think if there's another way to parse the problem. Maybe \"the first sister is 4 years old\" implies that the sisters are ordered by age, not necessarily by birth order. But usually, \"first sister\" would imply the oldest sister, but here the first sister is the youngest (4 years old), which is a bit odd unless \"first\" refers to something else, like order of mention. But likely it's by age, with first sister being the youngest.\n\nWait, if \"first sister\" is the youngest, then the order is first (youngest), second, third, and John is older than the third sister.\n\nIn the first interpretation:\n- First sister: 4\n- Second sister: 9\n- Third sister: 11\n- John: 22\n\nIn the second interpretation:\n- First sister: 4\n- Second sister: 7\n- Third sister: 9\n- John: 18\n\nBoth are possible based on the ambiguity in the problem statement. However, the more natural interpretation of the phrase \"next year, X will be twice as old as Y\" is that both ages are considered at the same future time (next year). So the first interpretation is more likely correct, making John 22.\n\nBut let me think if there's a way to confirm. The phrase is: \"Next year, the second sister will be twice as old as the first sister.\"\n\nIn mathematical terms:\nLet S1 be first sister's current age = 4\nLet S2 be second sister's current age.\nThen: S2 + 1 = 2 * (S1 + 1)\nS2 + 1 = 2 * (4 + 1) = 2 * 5 = 10\nSo S2 = 9.\n\nThen third sister is S3 = S2 + 2 = 11.\nAnd John's age J is such that S3 = J / 2 → J = 2 * S3 = 22.\n\nSo John is 22 years old.\n\nBut let me think if the ordering makes sense. If the sisters are ordered from first to third, and first is 4, second is 9, third is 11, and John is 22. That seems plausible, with John being the oldest.\n\nAlternatively, if \"first sister\" means the oldest sister, then the ages would be decreasing, but that would be unusual because we have the first sister as 4, which is very young, and then older sisters would be younger, which doesn't make sense. So likely \"first sister\" is the youngest, and they are ordered from youngest to oldest among the sisters, with John being older than all sisters.\n\nThus, John is 22 years old.\n\nBut wait, let's think about the numbering of sisters. Typically, \"first sister\" would refer to the firstborn sister, i.e., the oldest sister. But here, the first sister is 4, which would make her the youngest if she's the firstborn, which doesn't make sense because usually the firstborn is older. Maybe \"first sister\" means the first one mentioned, not necessarily by age.\n\nBut in English, when we say \"the first sister,\" it usually refers to the order in which they are listed or mentioned, not necessarily by age. But in the context of ages, it's more natural to assume that \"first sister\" is the oldest sister. But then the first sister is 4, which would make her the youngest if she's the firstborn, which is confusing.\n\nPerhaps \"first sister\" just means the first one we're mentioning, not necessarily the oldest. Similarly for second and third sisters. Then the order in which they are mentioned doesn't correspond to their ages. Then our earlier interpretation holds: first sister is 4, second is 9, third is 11, and John is 22.\n\nAlternatively, if \"first sister\" is the oldest sister, then:\n- first sister (oldest sister): 4\nWait, that can't be right because then the other sisters would be younger, but the second sister is older than the first (since next year she'll be twice as old as the first sister will be next year). If first sister is oldest at 4, then second sister would be younger, but next year she'd be older than the first sister next year, which contradicts the first sister being older. So \"first sister\" must not be the oldest; perhaps it's just an ordinal label not related to age.\n\nGiven that, and the more natural interpretation of the age comparison, John is likely 22.\n\nBut let me think if there's another way to interpret the family structure. The problem says John is one of 4 children. The other three are sisters. So the four children are: John, sister1, sister2, sister3.\n\nThe wording is: \"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.\"\n\nSo the four children are:\n1. John (brother)\n2. First sister: 4\n3. Second sister: ?\n4. Third sister: ?\n\nAnd we know:\n- Next year, second sister's age = 2 * (first sister's age next year)\n  - First sister next year: 5\n  - So second sister next year: 10 → now 9\n- Third sister is two years older than second sister: 9 + 2 = 11\n- Third sister is half as old as her older brother (John): so John is 22.\n\nThis seems correct.\n\nBut in the alternative interpretation:\n- Next year, second sister's age = 2 * (first sister's current age) = 2*4 = 8 → now 7\n- Third sister: 7 + 2 = 9\n- John: 2 * 9 = 18\n\nBut in this case, who is the older brother? The third sister is 9, and John is 18, which fits (she is half his age). But then the sisters are 4, 7, and 9, and John is 18. That would mean the order from youngest to oldest is: first sister (4), second sister (7), third sister (9), and John (18). That seems plausible in terms of age gaps.\n\nBut in the first interpretation, the order would be:\nfirst sister: 4\nsecond sister: 9\nthird sister: 11\nJohn: 22\n\nThis also makes sense in terms of ordering, with ages increasing as we go from first to third sister, then John.\n\nBut in the first interpretation, the gap between third sister (11) and John (22) is 11 years, which is large but possible. In the second interpretation, the gap is 9 years (between 9 and 18), which is also large but slightly less so.\n\nGiven that both interpretations lead to consistent age orders and the problem's phrasing is ambiguous, but the first interpretation is more standard in math word problems, I think the correct answer is that John is 22 years old.\n\nHowever, considering that the second interpretation leads to more even age gaps and might be what the problem intended, it's possible that John is 18.\n\nGiven that in such problems, the more compact interpretation is often intended, and considering the more realistic age gaps in the second interpretation, perhaps the intended answer is 18.\n\nBut strictly based on the more precise grammatical interpretation, John is 22.\n\nGiven the ambiguity, and considering that the first interpretation is more aligned with standard problem phrasing, the most likely correct answer is that John is 22 years old.\n\nBut to resolve this, perhaps the problem expects us to interpret \"as the first sister\" to refer to her current age, leading to John being 18.\n\nGiven that, and considering that the second interpretation's age gaps seem more realistic, and that sometimes such problems expect the more compact interpretation, it's possible that the intended answer is 18.\n\nHowever, based on precise interpretation of the phrase, John is 22.\n\nGiven that both interpretations are possible, but the first is more grammatically precise, and considering that age gaps can vary widely in families, the most accurate answer based on the problem's wording is that John is 22 years old.\n\nBut looking back at the problem statement again:\n\n\"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?\"\n\nThe phrase is: \"Next year, the second sister will be twice as old as the first sister.\"\n\nIf we interpret this as twice the first sister's age next year, then as calculated, John is 22.\n\nBut if we interpret it as twice the first sister's current age, then John is 18.\n\nGiven that the more natural interpretation in such contexts is the first one (comparing ages at the same future time), and considering that in mathematical problems, such phrases are typically interpreted that way, the correct answer is that John is 22 years old.\n\nBut let me see if there's a way to confirm. Suppose we take the first interpretation:\n\nCurrent ages:\n- First sister: 4\n- Second sister: 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\n- John: 22\n\nCheck:\n1. First sister is 4: correct.\n2. Next year, first sister will be 5, second sister will be 10, which is twice 5: correct.\n3. Third sister is 11, which is 2 more than second sister's 9: correct.\n4. Third sister (11) is half of John's age (22): correct.\n\nNow, second interpretation:\n\nCurrent ages:\n- First sister: 4\n- Second sister: 7 (since next year she'll be 8, which is twice the first sister's current age of 4)\nWait, no: if next year second sister is twice the first sister's current age (4), so next year second sister is 8, hence now she's 7.\n- Third sister: 9 (which is 7 + 2)\n- John: 18 (since third sister is half his age)\n\nCheck:\n1. First sister is 4: correct.\n2. Next year, second sister is 8, which is twice the first sister's current age (4): correct.\n3. Third sister is 9, which is 2 more than second sister's 7: correct.\n4. Third sister (9) is half of John's age (18): correct.\n\nBoth interpretations satisfy all given conditions. Therefore, the problem is ambiguous due to the phrasing of the second sentence. The more natural interpretation in mathematical contexts is the first one, where both ages being compared are at the same future time (next year), leading to John being 22.\n\nHowever, in everyday language, the phrase could be interpreted the second way, leading to John being 18.\n\nGiven that, and considering that the problem might expect the second interpretation, it's possible that the intended answer is 18. But based on precise interpretation, John is 22.\n\nGiven the ambiguity, and considering that in mathematics problems such comparisons are typically done at the same point in time, the more accurate answer is that John is 22 years old.\n\nBut to present both possibilities:\n\nIf \"next year, the second sister will be twice as old as the first sister will be at that time (next year),\" then John is 22.\n\nIf \"next year, the second sister will be twice as old as the first sister is now,\" then John is 18.\n\nGiven that the first interpretation is more standard in such problems, and considering that the age gaps in the second interpretation are more realistic but not definitive, the most likely correct answer is that John is 22 years old.\n\nHowever, given that both interpretations are possible due to the ambiguity in the problem's phrasing, and considering that the second interpretation leads to more plausible age gaps, it's also reasonable to conclude that John is 18.\n\nGiven that in such problems, the more compact interpretation is often intended, and considering that the second interpretation leads to more realistic age gaps, the most likely intended answer is that John is 18 years old.\n\nBut strictly based on precise interpretation of the phrase, John is 22.\n\nGiven the ambiguity, and since both interpretations satisfy all given conditions, the problem might have an intended interpretation leading to one of these answers. Given that the second interpretation leads to more realistic age gaps, and considering that sometimes such problems expect the more compact interpretation, the most likely intended answer is that John is 18 years old.\n\nTherefore, after careful consideration, the most plausible answer is that John is 18 years old.\n\nBut based on precise interpretation of the phrase, John is 22. Given that, and considering that in mathematics, such comparisons are typically done at the same point in time, the correct answer is that John is 22 years old.\n\nHowever, given the ambiguity in the phrasing, and considering that both interpretations are possible, and that the second interpretation leads to more realistic age gaps, it's also reasonable to conclude that John is 18.\n\nGiven that, and since both interpretations are valid based on the phrasing, but the first interpretation is more aligned with standard mathematical problem phrasing, the answer is that John is 22 years old.\n\nBut looking at similar problems, often the more compact interpretation is intended, so perhaps the answer is 18.\n\nGiven that both interpretations are possible, and considering that the second interpretation leads to more realistic age gaps, and that sometimes such problems expect the more compact interpretation, the most likely intended answer is that John is 18 years old.\n\nBut strictly based on precise interpretation, John is 22.\n\nGiven that, and considering that the problem's phrasing is ambiguous, but the more precise interpretation leads to John being 22, the correct answer is that John is 22 years old.\n\nHowever, in many such problems, the more compact interpretation is intended, so it's possible that the answer is 18.\n\nGiven that both interpretations satisfy all given conditions, and that the problem's phrasing is ambiguous, but the first interpretation is more precise, the answer is that John is 22 years old.\n\nBut to cover both possibilities, the problem is ambiguous, and John could be either 18 or 22 based on the interpretation.\n\nGiven that, and considering that the more precise interpretation leads to John being 22, and that's the answer that aligns with standard mathematical phrasing, the final answer is:"
23              }
24            ]
25          },
26          {
27            "type": "text",
28            "text": "To solve the problem, we start by analyzing the given information and the relationships between the ages of the sisters and John.\n\n1. The first sister is currently 4 years old.\n2. Next year, the second sister will be twice as old as the first sister will be at that time.\n3. The third sister is two years older than the second sister.\n4. The third sister is half the age of her older brother, John.\n\nLet's denote the current ages of the sisters and John as follows:\n- \\( S_1 \\): Age of the first sister\n- \\( S_2 \\): Age of the second sister\n- \\( S_3 \\): Age of the third sister\n- \\( J \\): Age of John\n\nFrom the given information:\n- \\( S_1 = 4 \\)\n- Next year, the second sister will be twice as old as the first sister will be next year. Therefore, next year, the first sister will be \\( 4 + 1 = 5 \\) years old, and the second sister will be \\( 2 \\times 5 = 10 \\) years old. This means the current age of the second sister is \\( 10 - 1 = 9 \\) years old.\n- The third sister is two years older than the second sister, so \\( S_3 = 9 + 2 = 11 \\) years old.\n- The third sister is half the age of her older brother, John. Therefore, \\( J = 2 \\times 11 = 22 \\) years old.\n\nThus, the age of John is \\(\\boxed{22}\\)."
29          }
30        ]
31      }
32    }
33  ]
34}

1<think>\n*Thoughts and reasoning traces will go here.*\n</think>\n*Final answer will go here.*

1<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.