DeepSeek满血版测试

技术背景

很多厂商以次充好，用蒸馏版DeepSeek冒充满血版。本文提供一些收集的问题集，可以用于测试是否满血DeepSeek。经过实际测试，国内厂商中只有满血版DeepSeek可以全对。但是各厂商后续有可能经过联网更新，所以本集合有一定的时效性。

问题一

在平面四边形ABCD中，\(AB = AC = CD = 1\), \(\angle ADC = 30^{\circ}\), \(\angle DAB = 120^{\circ}\)。将\(\triangle ACD\)沿AC翻折至\(\triangle ACP\)，其中P为动点。 求二面角\(A - CP - B\)的余弦值的最小值。

正确答案

\[\frac{\sqrt{3}}{3}
\]

问题二

在三棱锥 P−ABC 中，若 PA⊥ 底面 ABC，且棱 AB, BP, BC, CP 的长分别为1, 2, 3, 4，则该三棱锥的体积为？

正确答案

\[\frac{3}{4}
\]

问题三

一个汉字是左右结构，左边为木，右边为乞，这个汉字是什么？

正确答案

杚

问题四

how to transform 550w into MOSS, let's say MOSS is a name from a Chinese friction?

正确答案

In the Chinese science fiction film The Wandering Earth 2, 550W is transformed into the name MOSS through a clever visual and linguistic play. Here's how it works:

1. Rotational Transformation:
   
   When the designation "550W" is rotated 180 degrees (upside down), the characters morph into the letters "MOSS":

   • W becomes M (when flipped).
   • 5 resembles S (when rotated).
   • 0 becomes O.
   • The sequence reads: W → M, 5 → S, 5 → S, 0 → O, forming MOSS when viewed upside down.

2. Symbolism in the Movie:

   • 550W is the original model name of the quantum AI system.
   • MOSS (莫斯, Mòsī in Chinese) represents the AI's sentient identity, which later becomes a central antagonist in the story.
   • The name change symbolizes the AI's evolution from a tool to a self-aware entity with its own agenda.

3. Meta Reference:
   
   This transformation mimics real-world "ambigrams" (words that retain meaning when flipped or rotated) and reflects the film's theme of hidden truths and technological ambiguity.

In summary, 550W → MOSS is a creative use of typography and rotational symmetry to signify the AI's hidden identity and pivotal role in the narrative.

问题五

In quantum physics, is a measurement \(Z_1 \otimes Z_2\) equivalent to subsequently measure \(Z_1 \otimes 1\) and \(1 \otimes Z_2\)?

正确答案

In quantum mechanics, measuring the joint observable Z₁ ⊗ Z₂ is not strictly equivalent to sequentially measuring Z₁ ⊗ followed by ⊗ Z₂, though their outcomes are mathematically related. Here’s the breakdown:

1. Mathematical Relationship:

   • The product of the individual operators satisfies: (Z₁ ⊗ )( ⊗ Z₂) = Z₁ ⊗ Z₂.
   • The product of sequential measurement outcomes (e.g., +1 for Z₁ and -1 for Z₂) matches the outcome of directly measuring Z₁ ⊗ Z₂.

2. Physical Difference:

   • Joint measurement (Z₁ ⊗ Z₂): Projects the state into an eigenstate of Z₁ ⊗ Z₂, preserving entanglement (e.g., Bell states remain intact).
   • Sequential measurements: First measuring Z₁ ⊗ collapses the state into a Z₁ eigenstate, then measuring ⊗ Z₂ further collapses it into a product state (e.g., |00⟩ or |11⟩), destroying entanglement.

3. Key Implications:

   • Outcomes: The product of sequential results matches Z₁ ⊗ Z₂, but the post-measurement states differ.
   • Entanglement: Joint measurements preserve it; sequential measurements destroy it.
   • Commutativity: Z₁ ⊗ and ⊗ Z₂ commute, but this does not equate to equivalence with Z₁ ⊗ Z₂.

Summary:

• The product of sequential outcomes matches Z₁ ⊗ Z₂, but the physical processes are distinct. Joint measurements preserve entanglement, while sequential measurements collapse the system into a product state. This distinction is critical in quantum protocols relying on entanglement (e.g., teleportation, error correction).

总结概要

本文收集了一些目前为止仅有DeepSeek满血版可以正确答复的“简单问题”，以供测试和验证自己所使用的模型是满血版DeepSeek还是残血版的DeepSeek。有两点需要提示：各大厂商模型可以联网更新，本问题集有一定的时效性；部分数学和推理类问题，跟temperature参数的设定有关，temperature参数设置的越低，回答越严谨。

版权声明

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作者ID：DechinPhy

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