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Concise Reasoning, Big Gains: Pruning Long Reasoning Trace with Difficulty-Aware Prompting

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Concise, difficulty-matched reasoning traces train better student models than eight times more verbose data.

desk verdict Useful dataset and a fair 25K-vs-25K comparison, but the paper's central claim about pruning is confounded with rewriting; the practical pipeline works, the mechanism is unproven. read the letter →

arxiv 2505.19716 v1 pith:XQMSJNDT submitted 2025-05-26 cs.AI

Yifan Wu , Jingze Shi , Bingheng Wu , Jiayi Zhang , Xiaotian Lin , Nan Tang , Yuyu Luo This is my paper
classification cs.AI
keywords chain-of-thoughtdistillationdifficulty-awarepromptingreasoningtracecompressiontokenefficiencyLiteCoTsupervisedfine-tuningmathmodels
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the long chain-of-thought traces used to distill reasoning abilities into smaller models are not just expensive; their uniform verbosity also teaches students to reason poorly. Its fix, difficulty-aware prompting (DAP), makes a teacher model classify each problem as simple, medium, or complex and then rewrite the original long solution into a shorter one whose structure and detail match that difficulty. The result is LiteCoT, a 100K-sample dataset whose solutions average roughly 720 tokens, about an order of magnitude shorter than standard distilled traces. Students fine-tuned on LiteCoT, the Liter models, match or beat models trained on 800K original long traces across 11 benchmarks while using far fewer inference tokens, including a first-attempt correct rate of 74.2% on AIME24 with about 5K inference tokens per problem. If the claim holds, concise difficulty-adaptive traces are a drop-in replacement for verbose traces in chain-of-thought distillation, improving both cost and accuracy.

What carries the argument

The load-bearing mechanism is the difficulty-aware prompt template, a three-tier instruction set that makes the teacher both grade the problem and compress its own solution to match the grade. The easy tier requests a direct solution and summary, the medium tier requests an initial approach, reflection, and improvement, and the hard tier requests subproblem decomposition, integration, and overall reflection. This single prompt performs the entire data curation without training an auxiliary compression model, and the resulting LiteCoT dataset is what is used for supervised fine-tuning of the Liter models.

What would settle it

Take a random sample of LiteCoT items and run the teacher on the original long trace and on the rewritten short trace with identical decoding settings, comparing final answers: if a nontrivial share of rewrites change the answer or omit a required step, the claim that pruning is lossless fails. A second check is to train only on problems the teacher labeled easy and medium and test on held-out hard problems; if AIME-level accuracy collapses, then the difficulty labels, not the shorter length, are doing the work.

Watch

Extended reading notes

Core claim

The central discovery is that pruning reasoning traces by difficulty, rather than leaving them uniformly long, makes the student better, not worse. In the DAP pipeline, the teacher receives each question together with its long trace, judges the difficulty, and rewrites the trace according to a three-level template: direct solution for simple problems, analysis-initial approach-reflection-improvement for medium ones, and decomposition into subproblems with integration and reflection for hard ones. Trained on 100K such rewrites, the Liter models outperform the same base models distilled on 800K original long traces, with the gains appearing consistently across model sizes from 1.5B to 32B. The paper concludes that uniform-length verbose traces teach overthinking, while concise difficulty-adaptive traces teach students to match reasoning effort to the problem.

Load-bearing premise

The whole method rests on the teacher's difficulty labels and shortened rewrites being faithful: if a hard problem is mislabeled easy, or the rewrite drops a necessary calculation, the student learns incomplete reasoning and the reported gains would not survive on harder or out-of-distribution problems.

Editorial extensions

If this is right

  • A student trained on 100K LiteCoT samples, averaging 720 tokens per solution, outperforms the same base model trained on 800K original long traces on 11 benchmarks.
  • Inference cost drops sharply: the 32B Liter reaches 74.2% Pass@1 on AIME24 with roughly 5K inference tokens per problem, fewer than comparable methods consume for lower accuracy.
  • The difficulty-adaptive trace style transfers across model scales from 1.5B to 32B and to a different base architecture (Llama3.1-8B), so the benefit is not tied to one model family.
  • Against other CoT compression approaches, such as Chain-of-Draft, LLMLingua-2, and budget-aware reasoning, the DAP-trained model keeps or improves accuracy while using less inference time on most tested benchmarks.
  • Verbose uniform traces are not merely costly; models trained on them are consistently less accurate than models trained on shorter, difficulty-matched traces.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if short traces train better students than long ones, then much of the verbosity in teacher traces is not harmless padding but a form of noise that imitation learning picks up; pruning is then data denoising, not just compression.
  • Beyond the paper: the same teacher-driven difficulty rewrite should be testable on verifiable domains such as code generation or planning, where the optimal trace length per difficulty can be measured directly by pass rates.
  • Beyond the paper: because the teacher supplies both the difficulty label and the rewrite, the pipeline would be stronger with an independent difficulty signal such as contest ratings or an external solver's step count, to check whether label errors cap the gains.
  • Beyond the paper: the paper reports downstream accuracy but not whether each rewritten trace preserves the original final answer; a programmatic answer check on the LiteCoT subset would separate the effect of pruning from the effect of rewriting errors.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes Difficulty-Aware Prompting (DAP), a pipeline in which a teacher model (DeepSeek-R1) assigns each problem a difficulty label and rewrites the original long chain-of-thought trace into a shorter, difficulty-adapted solution. The resulting dataset, LiteCoT (100K examples, averaging 720 tokens per solution), is used to fine-tune Qwen2.5-based student models (Liter 1.5B/7B/14B/32B). The authors report three experiments: (Exp-1) short vs. long CoT fine-tuning on the same 25K OpenThoughts questions; (Exp-2) comparison of Liter models with DeepSeek-R1-distilled and other mainstream reasoning models; (Exp-3) comparison with Chain-of-Draft, LLMLingua-2, and Budget-Aware reasoning. The central claim is that difficulty-pruned concise CoT traces are a drop-in replacement for verbose traces, yielding equal or better accuracy with an order-of-magnitude reduction in tokens and cost.

Significance. If the central claim were fully established, the paper would be a valuable contribution: it provides a simple prompt-based method to generate compact, difficulty-adaptive distillation data, and it releases code and the LiteCoT dataset. The detailed training configs in the appendix support reproducibility, and the evaluation across 11 benchmarks is broad. However, the evidence as presented supports the weaker claim that DAP-processed short traces train competitive student models; it does not isolate the contribution of trace-length pruning from the contribution of the teacher rewrite itself. The reader's and skeptic's concerns about confounded comparisons are well grounded. Given that the core method is an empirical data-curation pipeline, the missing control conditions are fixable within the paper's scope, which in my view calls for major revision rather than rejection.

major comments (5)
  1. [§3.1, Eqs. (2)-(3); Table 2] The DAP transform is defined as a full regeneration of the trace under a difficulty-specific template, not as a length-respecting edit. Consequently, Exp-1's short-vs-long comparison varies at least three factors at once: token count, structured section formatting (Analysis/Approach/Summary, etc.), and content changes introduced by the DeepSeek-R1 rewrite. The paper's central claim that 'pruning' the trace yields the gains is therefore not supported: no condition holds rewriting constant while varying length, and no condition holds length constant while varying difficulty-awareness. I request two control conditions: (i) a generic 'be concise' rewrite of the same Long CoT at matched token budget, and (ii) a difficulty-aware rewrite that preserves the original length. Without these, the gains in Table 2 cannot be attributed to pruning rather than to the teacher rewrite or template formatting.
  2. [§4.2.2, Table 3] The headline comparison of 100K LiteCoT with 800K DeepSeek-R1-Distilled models is confounded by data source and question set: LiteCoT is derived from 100K OpenThoughts samples, whereas DS-R1-Distilled models were trained on DeepSeek-R1's 800K outputs from a different question distribution. The abstract's statement that the student 'outperforms a model distilled on 800K original Long CoT samples' is a product-level comparison, not a controlled test of DAP. I ask the authors to add a baseline trained on the same 100K OpenThoughts raw Long CoT with the same training recipe and hyperparameters, and to clearly frame the 800K comparison as an external benchmark rather than as evidence for the pruning effect.
  3. [§4.2.3, Table 4] Exp-3 compares DAP-trained models with inference-time compression methods (Chain-of-Draft, LLMLingua-2, Budget-Aware) applied to a Vanilla model that has not been trained on any distilled traces. These are not alternative training-data-generation pipelines, so the comparison does not control for the teacher-rewrite confound identified above. To support the claim that DAP is a superior data-curation method, the authors should compare against other training-data pipelines, such as DLCoT or Long-Short CoT mixture SFT (references 20 and 27), using the same base model and the same training budget.
  4. [Tables 2-3, §4.2] No error bars, multiple seeds, or significance tests are reported, and several headline differences are within sampling noise on small benchmarks. In particular, AIME24 has only 30 problems: Table 3's Liter-32B vs. DS-R1-Distilled-32B AIME24 scores (76.7 vs. 72.6) are 23/30 vs. 22/30, and several Table 2 AIME24 differences (e.g., 3.3 vs. 0.0) are single-problem differences. The paper's claim of 'consistent' gains is stronger than the evidence supports; I request standard errors or per-seed results, and a discussion of which differences exceed noise.
  5. [§3.1 Step 2; Abstract] The paper asserts that the rewritten traces are 'concise yet complete reasoning traces,' but it does not validate the correctness or completeness of the rewritten solutions, nor does it report the distribution of difficulty labels produced by the teacher. If the teacher mislabels hard problems as easy, or if the rewrite omits a necessary calculation, the student will be trained on incomplete reasoning; downstream accuracy is only an indirect check. I ask the authors to report the difficulty-label statistics and to include a sample-level correctness audit (e.g., LLM-as-judge or automated verification on a subset) to support the completeness claim.
minor comments (5)
  1. [§4.1, Table 2] The base-model list in §4.1 does not include Qwen2.5-3B, but Table 2 and Figure 4 report results for 'QW-3B'. Please add the missing model to the setup or explain where it comes from.
  2. [Figure 5, §4.2.2; Table 3] There are internal inconsistencies in reported numbers: the text says Liter-7B reaches 60.6% on Math500, while Table 3 lists 93.8%; Figure 5 shows DeepSeek-R1-Distilled-32B at 48.0% on AIME24, while Table 3 reports 72.6%. These discrepancies need to be reconciled; otherwise the reader cannot trust which numbers are official and which are retested.
  3. [Table 2] The entry '1.61' in the College Math row for LM-8B under 'long' appears to be a typo (likely 16.1 or similar). Please check all numeric entries in Table 2 and Figure 5 for consistency.
  4. [References] Reference [33] (Choquette-Choo et al.) appears to be a differentially-private learning paper, not an OlympiadBench resource; please update the citation for the OlympiadBench dataset.
  5. [Author affiliation] The author affiliation 'Indepent Researcher' should read 'Independent Researcher.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DAP pipeline is an empirical data-curation method whose claims are tested on external benchmarks against independently trained baselines.

full rationale

The paper's central claim is that a student model trained on 100K difficulty-pruned short CoT traces (LiteCoT) outperforms a model trained on 800K original long CoT traces. This is an empirical comparison, not a derivation, and none of the benchmark numbers are constructed from the method's inputs. The difficulty labels in Eq. (1) are produced by the teacher model, but they are not fitted to the reported evaluation results; the evaluation is performed on external benchmarks (AIME24, MATH500, GPQA, etc.) using separate test-time inference. The short CoT rewrites in Eqs. (2)-(3) take the long CoT as input, but the output is a new teacher-generated trace under a difficulty-specific prompt; there is no equation that equates the claimed accuracy gain to the rewriting by construction. The most plausible circularity concern is that the same teacher model (DeepSeek-R1) generated the original long traces and also rewrote them, but this does not force the student-model outcomes: Exp-1 directly compares models trained on the original 25K long traces against models trained on the corresponding 25K DAP short traces from the same OpenThoughts samples, and the student accuracies are measured externally. The paper's self-citations ([16], [17], [18]) appear only in the related-work discussion and are not load-bearing for the main empirical result. The experimentally uncontrolled confound between length reduction, structured formatting, and teacher content rewriting is a real experimental-design criticism, but it is a correctness/validity concern rather than circularity: the paper does not define its prediction in terms of its inputs, nor does it fit a parameter and then rename it as a prediction. Under the stated rules, no circular step can be exhibited with a quoted equation that reduces to itself, so the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new physical or mathematical entities are introduced. The method relies on prompt design and teacher model behavior rather than fitted numerical constants. The hand-chosen values and unverified assumptions above are the main things the central claim rests on beyond the experimental pipeline.

free parameters (4)
  • Number of difficulty levels = 3 (easy, medium, hard)
    Hand-chosen prompt structure; no external calibration of the thresholds between levels.
  • Dataset size = 100K
    Hand-chosen scale for LiteCoT; the paper does not study sensitivity to this number.
  • Fine-tuning epochs = 3
    Taken from the Open-R1 recipe without ablation.
  • Learning rate = 5e-5
    Standard choice, not tuned per model in the paper.
assumptions (4)
  • domain assumption DeepSeek-R1's difficulty assessment is accurate enough for length-adaptive rewriting.
    Section 3.1 Step 2: the teacher labels each query as easy/medium/hard; no validation of these labels is provided.
  • domain assumption Rewritten concise CoT traces preserve the essential reasoning and are free of errors.
    Appendix A prompt instructs the teacher to produce 'concise yet complete' traces; no correctness check is reported.
  • domain assumption The 100K OpenThoughts samples are representative of the evaluation benchmarks.
    Section 4.1: the training split is described only as '100K OpenThoughts samples'; selection criteria are not given.
  • domain assumption Supervised fine-tuning on teacher CoT traces transfers reasoning ability.
    This is a standard result in prior work (e.g., DeepSeek-R1 distillation) and is adopted without re-derivation.

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Cite this review

Pith. "Pith review of Concise Reasoning, Big Gains: Pruning Long Reasoning Trace with Difficulty-Aware Prompting." pith.science (2026). https://pith.science/paper/XQMSJNDT

@misc{pith2026250519716,
  author       = {Pith},
  title        = {Pith review of: Concise Reasoning, Big Gains: Pruning Long Reasoning Trace with Difficulty-Aware Prompting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XQMSJNDT}},
  note         = {Machine review of arXiv:2505.19716}
}
abstract

Existing chain-of-thought (CoT) distillation methods can effectively transfer reasoning abilities to base models but suffer from two major limitations: excessive verbosity of reasoning traces and inadequate adaptability to problem difficulty. Long reasoning traces significantly increase inference costs, and uniform-length solutions prevent base models from learning adaptive reasoning strategies. To address these issues, we propose a difficulty-aware prompting (DAP) method to dynamically shorten reasoning traces without performance loss. In our approach, a large teacher model first judges each problem's difficulty and then rewrites its reasoning traces to an appropriate shorter length, yielding concise yet complete reasoning traces. Leveraging the DAP pipeline, we curate a distilled dataset called LiteCoT consisting of 100K concise reasoning examples, with solutions averaging only 720 tokens (an order of magnitude shorter than typical CoTs). Using LiteCoT, we distilled a new family of reasoning models called Liter (1.5B, 7B, and 32B) based on the Qwen2.5 architecture. Experiments show that a student model fine-tuned on just 100K of these difficulty-pruned CoT samples outperforms a model distilled on 800K original Long CoT samples, while significantly reducing training and inference costs. Our method also generalizes well: across 11 diverse benchmarks, the shorter difficulty-aware CoTs achieve equal or better accuracy than Long chains, using far fewer tokens. For example, on the challenging AIME24 exam, our approach reaches $74.2\%$ Pass@1 using only about 5K inference tokens, surpassing other methods that consume many more tokens. Our code and data are available at https://github.com/Evanwu1125/LiteCoT.

Figures

Figures reproduced from arXiv: 2505.19716 by the authors.

Figure 1
Figure 1. (a) Training tokens comparison of LiteCoT with prior distillation methods (32B model); [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Overview of the DAP pipeline. First, the DeepSeek R1 model generates initial Long CoT [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Token count distribution of LiteCoT compared with previous CoT distillation datasets. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Inference time vs. accuracy across eight benchmarks. Models trained with short CoT (filled [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Radar chart show the performance comparison of the Vanilla, DeepSeek-R1-Distilled, and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Scatter plots comparing inference time and accuracy of different methods across multiple [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Additional experiment results comparing inference time and accuracy of different methods [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

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Forward citations

Cited by 1 Pith paper

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    For simple problems: **Analysis:** [Understand the core elements and goals of the problem] **Approach:** [Propose direct solution methods] **Summary:** [Concisely summarize the solution approach and key points]

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    0,...,n-1

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    Set \( q = r \), leading to \( n = 7r + r = 8r \)

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    natural numbers,

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    \] Since \(a + b + c = 2p\), this simplifies to: \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq \frac{9}{2p}

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    \] Thus, the inequality \(h_1 + h_2 + h_3 \geq 9r\) is proven

    **Substitute into height sum**: \[ h_1 + h_2 + h_3 \geq 2pr \cdot \frac{9}{2p} = 9r. \] Thus, the inequality \(h_1 + h_2 + h_3 \geq 9r\) is proven. \[ \boxed{h_{1} + h_{2} + h_{3} \geq 9r} \] <|end_of_solution|> 21 solutions of medium problems in OpenThoughts <|begin_of_though...

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    Inradius r = \Delta/s = 6/6 = 1

    Area \ Delta = (3*4)/2 = 6. Inradius r = \Delta/s = 6/6 = 1. Heights: h1 = 2\ Delta/a = 12/3 = 4, h2 = 12/4 = 3, h3 = 12/5 = 2.4. Sum of heights: 4 + 3 + 2.4 = 9.4. 9r = 9*1 = 9. So 9.4 \geq 9, which holds. So the inequality is satisfied here. Another example: a = 2, b = 2, c ...

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    So \Del ta approaches 0, and r = \Delta/s approaches 0. The heights: h1 and h2 (correspo nding to sides a=1 and b=1) will be h1 = 2\Delta/a = 2\Delta/1 = 2\Del ta, h2 sim ilarly 2\Delta, and h3 = 2\Delta/c \approx 2\Delta/(2 - \epsilon) 27 \ap prox \Del ta. So sum of heights \...

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    Express the heights in terms of the area and sides

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    Express the inradius in terms of the area and semiperimeter

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    Formulate the inequality in terms of the sides and semiperimeter

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    Apply the AM-HM inequality to establish the required result

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    Therefore, the inequality \( h_1 + h_2 + h_3 \geq 9r \) is proven

    Verify with specific examples to ensure validity. Therefore, the inequality \( h_1 + h_2 + h_3 \geq 9r \) is proven. <|end_of_thought|> <|begin_of_solution|> To prove that the sum of the heights of a triangle \( h_1 + h_2 + h_3 \) is at l east nine times the inradius \( r \), ...

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    - Sum of heights: \( h_1 + h_2 + h_3 = 2\Delta\left(\frac{1}{a} + \ frac{1}{b} + \frac{1}{c}\right) \)

    **Express Heights and Inradius**: - Heights: \( h_a = \frac{2\Delta}{a}, \, h_b = \frac{2\Delta}{b}, \, h_c = \ frac{2\Delta}{c} \), where \( \Delta \) is the area and \( a, b, c \) 29 are the si des. - Sum of heights: \( h_1 + h_2 + h_3 = 2\Delta\left(\frac{1}{a} + \ frac{1}{...

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    \] Cancel \( \Delta \) and multiply through by \( s \): \[ 2s\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \geq 9

    **Formulate the Inequality**: Substitute \( h_1 + h_2 + h_3 \) and \( 9r \) into the inequality: \[ 2\Delta\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \geq \f rac{9\Delt a}{s}. \] Cancel \( \Delta \) and multiply through by \( s \): \[ 2s\left(\frac{1}{a} + \frac{1}{b...

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    **Simplify Using Semiperimeter**: Substitute \( s = \frac{a + b + c}{2} \): \[ (a + b + c)\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \ge q 9. \]

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    \] Equality holds if and only if \( a = b = c \) (equilateral triangle )

    **Apply the AM-HM Inequality**: The Arithmetic Mean-Harmonic Mean (AM-HM) inequality states: \[ \frac{a + b + c}{3} \geq \frac{3}{\frac{1}{a} + \frac{1}{b} + \frac {1}{c}}, \] which rearranges to: \[ (a + b + c)\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \ge q 9. \] E...

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    Examples and edge cas es confirm 30 the validity of the result

    **Conclusion**: The inequality \( h_1 + h_2 + h_3 \geq 9r \) follows directly from the AM-HM inequality applied to the sides of the triangle. Examples and edge cas es confirm 30 the validity of the result. **Final Answer**: \boxed{h_{1} + h_{2} + h_{3} \geq 9r} <|end_of_solution|> 31

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    So r = 1.984 / 3.5 \approx 0.567

    \approx 1.984. So r = 1.984 / 3.5 \approx 0.567. Heights: h1 = 2\ Delta/a \a pprox 2*1.984 /2 \approx 1.984, h2 same as h1, h3 = 2*1.984 /3 \approx 1.323. Su m \approx 1.984 + 1.984 + 1.323 \approx 5.291. 9r \approx 5.103. So 5. 291 \geq 5 .103. Holds as well. Wait, but accord...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.