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Qwen 3.5 9B Q4_K_M solved this using 10K tokens in 5 mins on a RX 7600.

The answer is exactly what you have posted. I am impressed by Qwen!

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How do you know it’s a valid solution? Are you able to verify it yourself?
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This is a math problem with a math solution. You verify it with math
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Interesting!

I just tried the quantized Q4_K_M from [1] in my RTX 2070 Super, it ran at 110 tok/s with 1800 tok/s prefill, and found the same solution to your prompt. It generated valid LaTeX for the answer but its reasoning trace uses mostly compact ASCII math notation. Took 3min 22s to answer, spending 22k tokens almost all on thinking.

[1] https://huggingface.co/prithivMLmods/VibeThinker-3B-GGUF

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How do we know the solution isn't in the weights though?
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