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QReasoner2.5-32B-Instruct

QReasoner2.5-32B-Instruct excels at deliberate thinking and careful reasoning through complex problems.

It is a normalized denoised fourier interpolation with the following configuration:

output_base_model: "Qwen/QwQ-32B"
output_dtype: "bfloat16"
finetune_merge:
  - { "model": "qihoo360/Light-R1-32B", "base": "Qwen/Qwen2.5-32B-Instruct", "alpha": 1.0 }
  - { "model": "qihoo360/TinyR1-32B-Preview", "base": "Qwen/Qwen2.5-32B", "alpha": 0.9 }
  - { "model": "Qwen/Qwen2.5-32B-Instruct", "base": "Qwen/Qwen2.5-32B", "alpha": 1.0 }
  - { "model": "OpenPipe/Deductive-Reasoning-Qwen-32B", "base": "Qwen/Qwen2.5-32B-Instruct", "alpha": 0.8 }
  - { "model": "Saxo/Linkbricks-Horizon-AI-Avengers-V1-32B", "base": "Qwen/Qwen2.5-32B-Instruct", "alpha": 0.5 }

What is this?

This is a reasoning-focused model that excels at deliberate thinking and problem-solving. QReasoner combines the strengths of QwQ, different types of R1 distillations, and a few other high quality models.

Is it good?

It is a thorough thinker that excels at multi-step reasoning problems. The model demonstrates exceptional reasoning capabilities, including complex problem solving and deductive reasoning. It's particularly adept at breaking down complex problems into manageable steps and exploring multiple solution paths before arriving at the optimal answer.

The following is from a IQ4 NL test:

<think>
Okay, so the problem is: using a 2-gallon bucket and a 5-gallon bucket, how do you get exactly 4 gallons in one of them. Hmm, I need to figure out the steps. Let me start by recalling similar problems. Usually, with these measuring puzzles, you fill one container and pour into the other, using their capacities to measure specific amounts. Let me think step by step.

First, the buckets are 2 and 5 gallons. The goal is to have exactly 4 gallons in one of them. Since 4 is less than 5, maybe the 5-gallon bucket is the one we need to fill partially? Or perhaps the 2-gallon? Wait, but 4 is twice 2, so maybe using the 2-gallon multiple times? Hmm, not sure yet.

Let me consider possible operations: filling a bucket, emptying it, pouring from one to the other until one is full or the other is empty. Since the buckets are different sizes, their combinations can measure specific amounts.

Let me try starting by filling the 5-gallon bucket. So fill the 5-gallon to the top. Then pour from the 5 into the 2-gallon. Since the 2 can only hold 2, pouring 2 gallons into the 2, leaving 5-2=3 in the 5. Then empty the 2-gallon. Now, the 5 has 3, and the 2 is empty. Then pour the remaining 3 from the 5 into the 2. Wait, but the 2 can hold 2, so pouring 3 into it would only take 2, leaving 1 in the 5. Hmm, that might be a path.

Wait, let's track this step by step.

First step:

1. Fill the 5-gallon bucket. Now 5 has 5, 2 has 0.

2. Pour from 5 into 2 until 2 is full. So 2 gets 2 gallons, so 5 now has 5-2=3. So 5:3, 2:2.

3. Empty the 2-gallon. Now 5:3, 2:0.

4. Pour the 3 gallons from 5 into 2. But the 2 can only take 2, so pouring 3 into 2 would fill it to 2, leaving 1 in the 5. So after step 4: 5 has 1, 2 has 2. Wait, no—if you pour from 5 (which has 3) into 2 (which is empty). The 2 can take 2, so you pour 2 gallons into 2, but the 5 only has 3. Wait, no—if you pour from 5 to 2 until the 2 is full. Wait, the 2 can hold up to 2. So if you have 3 in the 5, and you pour into the 2 which is empty, you can pour 2 into the 2, leaving 1 in the 5. So after pouring, 5 has 1, 2 has 2. Then if you empty the 2 again, then pour the remaining 1 from 5 into 2. Then 2 has 1, and 5 is empty. Then refill the 5, pour into 2 until it's full. Since 2 has 1, you can add 1 more. So pouring 1 gallon from 5 to 2, filling it. Then the 5 would have 5 -1=4. Ah! There we go. Let me map that.

Wait, let me retrace. Let's try this again step by step.

Alternative approach:

Start over:

1. Fill the 5-gallon bucket. (5:5, 2:0)

2. Pour into 2-gallon. So 5 now has 3, 2 has 2. (5:3, 2:2)

3. Empty the 2. (5:3, 2:0)

4. Pour from 5 to 2. Now, the 2 can take 2, but the 5 has 3. So pouring 2 into the 2 would leave 1 in the 5. Wait, but pouring until the 2 is full. So pouring 2 gallons, so 5 gives 2, leaving 1. Then 5:1, 2:2.

Then, empty the 2 again. (5:1, 2:0)

Pour from 5 to 2: the 5 has 1, so pouring that into 2 gives 1 in the 2. Then refill the 5: fill it again. Now, 5:5, 2:1. Then pour from 5 into 2 until it's full. The 2 can take 1 more (since it has 1). So pour 1 gallon from 5 to 2, filling the 2. Then the 5 would have 5 -1 =4. So that works. But that requires multiple steps.

Wait, let's write the steps:

1. Fill 5-gallon. (5,0)

2. Pour into 2-gallon: 5-2=3 in 5, 2 full. (3,2)

3. Empty 2: (3,0)

4. Pour from 5 to 2: 5 has 3, so pouring into 2 which can take 2. So 3-2=1 left in 5, and 2 in 2. So now (1,2)

5. Empty 2 again: (1,0)

6. Pour from 5 to 2: 1 gallon into 2. Now (0,1)

7. Fill 5-gallon again: (5,1)

8. Pour from 5 into 2 until 2 is full. The 2 can take 1 (since it has 1). So pour 1 into it, leaving 5-1=4 in 5. So now 5 has 4, and 2 has 2. So that's 4 in the 5-gallon. So that works. But that's 8 steps, which seems a bit long. But maybe there's a shorter way.

Alternatively, maybe starting by filling the 2-gallon first.

Alternative method:

1. Fill the 2-gallon. (0,2)

2. Pour into 5-gallon. 5 now has 2, 2 is empty. (2,0)

3. Repeat: fill 2 again, pour into 5. Now 5 has 4, 2 has 0. Because 5 can take up to 5, so first pour 2 into 5: 2+2=4. So after two fillings of 2 into 5, you have 4 in the 5. Wait, that might be easier.

Wait, let me see:

Option:

1. Fill the 2-gallon bucket, pour into 5. (2 in 5)

2. Fill 2 again, pour into 5 again. Now 5 has 4, since 2+2=4, which is under 5's capacity. So then the 5-gallon has 4. So that's it? Then you can just fill the 2 twice and pour into 5, resulting in 4 in the 5. Then 4 is the desired amount. So that seems simpler. Wait, but why did I think of the other method before?

Wait, maybe that's the case. Let me check again.

First approach:

If you fill the 2-gallon, pour into 5. Then fill 2 again, pour into 5 again. Now, 5 can hold 5, so after first pour, 2 into 5, 5 has 2. Then second pour, another 2 into 5, making 4. So 5 has 4, and 2 is empty. Wait, no—if you pour from 2 into 5 each time. So first step: Fill 2 (2), pour into 5: 5 has 2. Then fill 2 again (so 2 again), pour into 5. Now 5 has 2 + 2 =4. So then 5 has 4, and 2 is empty. So then, you can just do that. So the 5-gallon would have 4, which is the target. So that's much simpler. So why did I go through the prior longer steps?

Hmm, perhaps I confused it with other problems where the target is different. Wait, maybe that works here. But is that possible?

Wait, but the problem says "fill one of the buckets with exactly 4 gallons". So if you pour two times 2 into the 5, then the 5 has 4, and then you can just take that. So that would be the solution. So why do some other methods require more steps?

Wait, but maybe there is a catch here. Let me check again step by step.

Step 1: Fill the 2-gallon bucket. So 2 is full (2), 5 is empty.

Step 2: Pour from 2 into 5. Now 5 has 2, 2 is empty.

Step 3: Fill 2 again. Now 2 is full again (2), 5 has 2.

Step 4: Pour from 2 into 5 until 5 is full. Wait, but 5 can take up to 5. Currently, 5 has 2. So pouring into 5 from 2: the 5 can take 3 more. But the 2 has 2. So pouring all 2 into 5, resulting in 5 having 4, and 2 empty. So after step 4, 5 has 4, 2 is empty. Therefore, you have 4 in the 5-gallon bucket. So that's done in 4 steps. That seems straightforward. So why did I think of the prior method? Maybe I confused with a problem where you have to measure a different amount, like 3 gallons with 4 and 5, but here the answer might be simpler.

Wait, so is this the solution? If so, then that's the answer. But maybe I'm missing something here.

Wait, the problem is phrased as "how do you fill one of the buckets with exactly 4 gallons". So if you fill the 2 into the 5 twice, then the 5 has 4. So yes. So that's the solution.

But maybe the problem is presented as tricky, but perhaps the straightforward method works here. Hmm.

Alternatively, maybe there is a trick here. Let me see.

Wait, the 5-gallon bucket can hold up to 5, so pouring 2 twice gives 4, so that's correct. So that's possible. Therefore, the steps are:

Fill the 2-gallon bucket twice into the 5-gallon, resulting in 4 gallons in the 5. So that's the answer.

Wait, but maybe the problem is presented in a way that you have only one bucket of each? Wait, the question says "if you have one bucket that holds two gallons and another bucket that holds five gallons", so you have both. So the process is possible by filling the smaller one twice into the larger, getting 4. Hmm. So that would be the case. Then that's the solution. So why did I initially think of the longer steps?

Alternatively, perhaps I made a mistake in thinking that the 5 is being filled from the 2, but actually, maybe the steps are correct.

Alternatively, maybe the problem requires that you have to have exactly 4 in one of the buckets, so if you have the 5 gallon with 4, that's acceptable. So that would be the solution.

Alternatively, maybe the problem is intended to have the 4 in the 5-gallon bucket. So the steps are:

1. Fill the 2-gallon.

2. Pour into 5-gallon.

3. Repeat once more: fill 2, pour into 5. Now 5 has 4. So yes.

Therefore, that's the solution. So why do some sources say that for similar problems you need more steps? Wait, perhaps the confusion comes from different problems. For example, if you wanted 3 gallons with 5 and 3, but here the numbers are different.

Wait, let me verify again with the steps.

First, fill the 2, pour into 5. 2 in 5, 0 in 2.

Fill 2 again, pour into 5. Now, 5 has 4, 2 is empty. So that's it. So that's two transfers. So that's possible. So maybe the answer is that simple.

Alternatively, perhaps I'm missing some constraint. The problem says "fill one of the buckets with exactly 4 gallons". So perhaps you need to have 4 in the 5-gallon bucket, which is possible as above.

Alternatively, maybe you need to have 4 in the 2-gallon, but the 2 can only hold 2, so that's impossible. Therefore, the only way is to have 4 in the 5-gallon. Therefore, the solution is to pour two lots of 2 into it, totaling 4. Hence, that's straightforward.

Hmm. Maybe that's the case. So perhaps the answer is:

Fill the 2-gallon bucket twice into the 5-gallon bucket, resulting in 4 gallons in the 5-gallon.

But let me see if there's another way. For instance, filling the 5 first and pouring into the 2, but that might take longer steps, but maybe the question expects the shorter method. Since the straightforward way works, that's the answer.

Alternatively, perhaps there's a trick here. Let me confirm with an example.

Suppose you have a 5 and 2. To get 4 in the 5.

Yes: Fill 2, pour into 5 (5 has 2). Fill 2 again, pour into 5 again. Now 5 has 4. Done. So that's two fillings and two pourings.

Alternatively, maybe that's the correct answer. So then why did I initially think of the longer method? Maybe I overcomplicated it.

Alternatively, perhaps the problem requires using the 5-gallon bucket to measure, but in that case, the above method is sufficient.

Alternatively, maybe the problem is presented in a different way, but perhaps that's the solution.

Alternatively, perhaps the question is a trick question, where you can just fill the 5-gallon and then pour out 1 gallon somehow, but how?

Wait, if you need 4 in the 5, then pouring out 1. But how? If you have the 5 filled to 5, then pour into the 2 until it's full. So 5 - 2 = 3, but that leaves 3. Hmm, not helpful.

Alternatively, maybe the method of filling the 5, pouring into 2 twice, but that might not get to 4.

Alternatively, maybe my first approach was overcomplicating, and the correct answer is simply filling the 2 into the 5 twice.

Therefore, the answer is:

Fill the 2-gallon bucket twice and pour each time into the 5-gallon bucket. The 5-gallon will then contain exactly 4 gallons.

Alternatively, step-by-step instructions:

1. Fill the 2-gallon bucket.

2. Pour the 2 gallons into the 5-gallon bucket.

3. Fill the 2-gallon bucket again.

4. Pour from the 2-gallon into the 5-gallon until it's full. However, wait—if the 5-gallon can only take 3 more gallons (since it already has 2), but the second pour is 2 gallons again. Wait, but 2 + 2 =4, which is under 5. Wait, hold on—if you pour the second 2 into the 5, the total is 4. Since the 5 can hold up to 5, you can just pour the entire 2 into it. So in that case, the 5 would have 4, and that's it. Therefore, you don't need to pour until the 5 is full. So actually, you can just fill the 2 twice into the 5, resulting in 4. Therefore, that's the answer. Hence, the steps are straightforward.

Alternatively, perhaps there's a gotcha here. Let me check again.

Suppose the problem is to measure exactly 4 gallons using only those two buckets. The standard way is that sometimes you have to fill or empty. But in this case, if you need 4 in the 5-gallon, then yes, just putting two 2s in it gives 4. So that's the simplest solution. Therefore, maybe that's the answer.

Alternatively, maybe I need to think that the user might have intended the other method where you use the 5 to measure, but perhaps the answer is that.

Alternatively, perhaps some people might think that you need to have the 4 in the 2-gallon, but that's impossible since it's only 2 gallons. Hence, the only possible is in the 5. Hence, the steps above.

Alternatively, maybe the problem requires that you have to have 4 in one of them through some other operation. Let me see.

Alternatively, perhaps the problem is presented as "how do you measure 4 gallons", so the answer is as above.

Therefore, the answer is to fill the 2-gallon twice into the 5-gallon, resulting in 4 gallons in the 5.

Alternatively, perhaps the steps should be written as:

- Fill the 5-gallon bucket, pour into the 2-gallon, leaving 3, then empty the 2, pour the 3 into the 2, then fill the 5 again. Hmm, but that might be for a different measurement.

Alternatively, let's see the two methods:

Method 1: Fill 2 into 5 twice, get 4 in 5. Easy.

Method 2: The longer method via filling 5, pouring into 2, etc., ending up with 1 in 5, then doing other steps to get 4. Wait, in the first approach I thought of earlier, you end up with 4 in the 5 after 8 steps, but the second method is shorter.

Therefore, the first method (Method 1) is the correct and simplest way.

Therefore, perhaps the answer is simply filling the 2-gallon twice into the 5, resulting in 4. So the steps are:

1. Fill the 2-gallon bucket.

2. Pour its contents into the 5-gallon bucket.

3. Repeat steps 1 and 2 once more. After the second pour, the 5-gallon bucket will have exactly 4 gallons.

Therefore, that's the solution.

Alternatively, maybe the problem is presented in a way that you have to use the buckets without having an unlimited water supply. Wait, the question says "fill one of the buckets with exactly 4 gallons". So perhaps you can only use the two buckets and the water source. So assuming you have a tap or something to fill them. So you can fill from the source, so the above method is possible.

Alternatively, maybe the problem is similar to the classic 4 gallons with 3 and 5, but here with 2 and 5. Hmm. Let me see.

Wait, in the classic problem, with a 3 and 5, to get 4, you might do different steps, but here with 2 and 5, it's easier.

Alternatively, perhaps I need to confirm once again.

Suppose:

Start with empty buckets.

Step 1: Fill the 2-gallon from the source.

Step 2: Pour the 2 into the 5. Now 5 has 2, 2 is empty.

Step 3: Fill the 2 again.

Step 4: Pour into the 5 until it's full. Wait, the 5 can take 5 - 2 =3 more. But the 2 has 2. So you can pour all 2 into 5, making 5 have 4, and 2 empty. So after step 4, the 5 has 4. Therefore, that's the desired amount. Therefore, yes, exactly 4 in the 5-gallon.

Therefore, the answer is that. Hence, the steps are as such. So this seems correct.

Alternatively, perhaps the confusion is that if you fill the 5 first, but the above method is more straightforward.

Therefore, the solution is to fill the 2-gallon twice into the 5, resulting in 4. Therefore, the answer is the steps outlined.
</think>

To measure exactly 4 gallons using a 2-gallon and a 5-gallon bucket, follow these steps:

1. **Fill the 2-gallon bucket** completely.  
2. **Pour the 2 gallons into the 5-gallon bucket**. The 5-gallon bucket now has 2 gallons.  
3. **Fill the 2-gallon bucket again**.  
4. **Pour the second 2 gallons into the 5-gallon bucket**. The 5-gallon bucket now holds **4 gallons total** (2 + 2).  

The 5-gallon bucket will now contain exactly **4 gallons**.  

**Steps summarized:**  
- Fill the 2-gallon bucket twice and transfer each portion to the 5-gallon bucket.  
- After two transfers, the 5-gallon bucket will have **4 gallons**.  

This method works because adding 2 gallons twice fills the 5-gallon bucket to 4 gallons without exceeding its capacity.  

✅ **Final Result:** The 5-gallon bucket contains **4 gallons**.

Citation

If you find our work helpful, feel free to give us a cite.

@misc{qreasoner2.5-32b-instruct,
    title = {QReasoner2.5-32B-Instruct},
    url = {https://huggingface.co/maldv/QReasoner2.5-32B-Instruct},
    author = {Praxis Maldevide},
    month = {March},
    year = {2025}
}