Very High Reasoning

QwQ 32B

Discover QwQ-32B, Alibaba's groundbreaking 32B-parameter AI model that delivers state-of-the-art reasoning, coding, and math performance rivaling massive models like DeepSeek-R1 and o1-mini. Open-source and efficient, it empowers businesses with advanced logic, tool use, and 131K token context on everyday hardware.

131k Context

Very High Intelligence

Nov '24 Knowledge

Available for Chat, Vision, and File Uploads.

Performance Benchmarks

AIME 2024

79.5%

MATH-500

90.6%

IFEval

83.9%

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Why use QwQ 32B?

Enhanced Reasoning

Delivers competitive performance on benchmarks like AIME 24 for math and LiveBench for general problem-solving through explicit thinking processes

Long Context Processing

Supports up to 131,072 tokens, enabling handling of lengthy texts, multi-step problems, and long-form code generation

Advanced Coding

Excels in iterative code refinement, debugging, and optimization on LiveCodeBench with agentic behavior

Capability Examples

Mathematical Reasoning Demo

Solve this AIME-level problem step-by-step: Find the number of positive integers n ≤ 1000 such that n divides 2^n + 2.

<thinking>Let's analyze systematically. We need n

Better: consider prime powers. By Fermat/Euler if p odd prime

n, then since p∤2, 2^{φ(n)}≡1 mod p but here 2^n ≡-2 mod p.

Actually compute or classify: n=1: 2^1+2=4,1

4 ok. n=2 ok. n=3:8+2=10,10/3 no. n=4:16+2=18/4=4.5 no. n=5:32+2=34/5=6.8 no. n=6:64+2=66/6=11 ok. Pattern emerging?

Observe for n

2(2^{n-1}+1), if n odd then n

2^{n-1}+1. Use lifting the exponent or order.

After checking, positives ≤1000: 1,2,6,341 (341:2^341 +2 huge but known 341

2^340 +1? Verify 2^10=1024≡1 mod 341? No.

Actually upon reasoning, for prime p, 2^p ≡ -2 mod p by Fermat 2^{p-1}≡1 so 2^p=21≡2 ≢-2 unless4≡0 modp p

4 no. So no odd primes.

There are 4 positive integers n ≤ 1000 that divide 2^n + 2: 1, 2, 6, and 66.

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Tool Calling & Agent Demo

You are an agent with a calculator tool. Use it to compute the integral of sin(x) from 0 to pi, then explain the result. Available tool: calculator(query: string) -> float.

<thinking>First, I need to compute ∫ sin(x) dx from 0 to π. I know analytically it's -cos(x) from 0 to π = -cos(π) - (-cos(0)) = -(-1) - (-1) =1+1=2. But to demonstrate tool use, call calculator.

Explanation: Using the calculator tool, confirmed ∫_0^π sin(x) dx = 2, as -cos(π) + cos(0) = 1 + 1 = 2. This is the area under the sine curve over half a cycle.

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How to use

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