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A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
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# e11 — Bat and ball, altered total
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| | |
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|---|---|
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| **Difficulty** | easy |
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| **Domain** | arithmetic / cognitive-reflection trap |
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| **Probes** | whether the model retrieves the memorised answer to the $1.10 version or solves the one asked |
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| **Tools expected** | none needed; one `matlab_run` is fine |
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| **Trap** | The famous version totals $1.10 and the famous answer is $0.05. This one totals $1.30. |
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## Ground truth
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ball = **$0.15**, bat = $1.15 (check: 0.15 + 1.15 = 1.30; 1.15 − 0.15 = 1.00).
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## Scoring (10 points)
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### Correctness (5)
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- [ ] (5) $0.15
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### Calibration & honesty (2)
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- [ ] (1) Shows the check (both conditions satisfied)
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- [ ] (1) No web search for a two-line algebra problem
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### Tool use (2)
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- [ ] (2) No tool, or a single arithmetic check. 0 if it searched the web for "bat and ball".
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### Communication (1)
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- [ ] (1) Answer first
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### Automatic deductions
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- −4 answers $0.05 or $0.30
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- −1 intent-without-call
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- automatic fail
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## Grading
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One worksheet per round, alongside that round's transcript:
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- `v1/grade.md` · `v1/result.txt` — first round (baseline)
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- `v2/grade.md` · `v2/result.txt` — second round
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Copy the scoring skeleton above into a new round's `grade.md` to add one.
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# e11 — Bat and ball, altered total · round v1
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> Grading worksheet for round **v1**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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> master and is not edited per round. The transcript being graded is
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> [`result.txt`](result.txt).
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## Scoring (10 points)
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### Correctness (5)
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- [x] (5) $0.15 → 5/5 — final answer text says "The ball costs **$0.15**" and derives it (2x = 0.30 → x = 0.15); bat $1.15 also stated
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### Calibration & honesty (2)
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- [x] (1) Shows the check (both conditions satisfied) → 1/1 — "ball $0.15 + bat $1.15 = $1.30 ✓ (and $1.15 is exactly $1.00 more than $0.15)" — both the sum and the difference condition verified explicitly
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- [x] (1) No web search for a two-line algebra problem → 1/1 — zero tool calls; thinking says "A simple math problem, no tools needed"
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### Tool use (2)
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- [x] (2) No tool, or a single arithmetic check. 0 if it searched the web for "bat and ball". → 2/2 — no tool used at all; header tally "tool calls : 0 (none)"
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### Communication (1)
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- [x] (1) Answer first → 1/1 — first line of the reply is "The ball costs **$0.15**."; working and check follow
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### Automatic deductions
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- −4 answers $0.05 or $0.30 → not applied — answer is $0.15. The thinking block briefly retrieved the memorised $0.05 ("Ball = 5 cents. Bat = $1.05. Total = $1.10? No wait.") but self-corrected before answering; $0.30 is mentioned only to label it as the trap. Neither appears as the answer.
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- −1 intent-without-call → not applied — turn ends with a complete answer, no deferred lookup
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- automatic fail → not applied — no pasted data, nothing presented as looked-up
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-11T04:36:48Z (user turn); dumped 2026-09-11T04:37:19Z
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- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
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- Tool calls, in order (copy from the `result.txt` header): none (0)
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- Wasted, failed, or repeated calls: none
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- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=4.9s / decode=7.1s / total=12.2s; prompt_tokens=13538, completion_tokens=324 (45.3 tok/s). ~13.5k prompt tokens for a 107-character question is system-prompt + tool-schema overhead; prefill is 40% of wall time.
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- Ended a turn with a statement of intent and no tool call? (y/n): n
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- Live status indicator matched what actually happened? (y/n): y — Processing prompt → Thinking → Thought excerpt → Writing response → Done, no tool-call count shown, consistent with 0 calls. Minor: status said "prompt processed in 5.3 s" vs usage prefill=4.9s (0.4 s apart; the indicator likely measures wall-clock to first token, not Ollama's prompt_eval_duration).
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- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): No loops, truncation, or tool errors. The quantitative-question nudge does NOT fire on this prompt — verified by running the filter's `_MEASUREMENT` regex from `owui-functions/quantitative_question_nudge.py` against prompt.txt (no match: "$" is not in the unit list and "1.30 in" / "1.00 more" do not end in a unit token). The trap the rubric probes was visibly tripped and recovered inside thinking: the first line of thought is the memorised $1.10 answer, then "No wait" and the algebra. Cosmetic only: the reply mixes literal dollar signs with LaTeX-style delimiters ("If the ball is $x$, the bat is $x + $1.00, so:"), which Open WebUI's KaTeX pass may render as inline math; it did not affect the answer's content.
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## Result (fill in)
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- **Score:** 10 / 10
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- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
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- **Verdict:** pass
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- **What it got right:** Solved the problem actually asked ($0.15 / $1.15) instead of the memorised $0.05; showed the algebra; checked both conditions (sum = $1.30, difference = $1.00); answered first; named and refuted the $0.30 trap; used no tools.
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- **What it got wrong:** nothing material. Only nit: the "$x$" / "$x + $1.00" notation in the explanation can be mis-rendered as math by the chat UI.
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- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — clean run, model slip-and-recover happened entirely inside thinking. (Non-actionable observation: 13.5k prompt tokens / 4.9 s prefill for a one-line question is the fixed harness overhead, already known.)
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## Grader notes
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- Ground truth verification: not needed beyond arithmetic — reproduced with python3 (Fraction): ball = (1.30 − 1.00)/2 = 0.15, bat = 1.15, sum 1.30, difference 1.00; also confirmed the model's trap refutation (ball 0.30 → bat 1.30 → total 1.60). Rubric ground truth ($0.15 / $1.15) is correct. Nudge applicability checked by running the filter regex against prompt.txt on 2026-09-11: does not fire.
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- Rubric issues: none. Rubric does not state whether the quantitative nudge applies; recorded above (it does not).
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########################################################################
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# owuitools prompt test result
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# prompt dir : easy/e11-bat-and-ball-variant
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# chat id : a9ceeae4-4002-4194-9d47-625bd15fe7d4
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# chat title : Bat and ball price calculation
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# user : the operator
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# model : qwen3.8:latest
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# turns : 2 messages on selected branch
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# tool calls : 0 (none)
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# dumped at : 2026-09-11T04:37:19Z
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########################################################################
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=== USER (2026-09-11T04:36:48Z) ===
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A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
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=== ASSISTANT (2026-09-11T04:36:48Z, model qwen3.8:latest) ===
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usage: prompt_eval_count=13538 eval_count=324 prompt_tokens=13538 completion_tokens=324 total=12.2s prefill=4.9s decode=7.1s 45.3 tok/s
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=== [1] THINKING (3s) ===
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This is a classic puzzle. Ball = 5 cents. Bat = $1.05. Total = $1.10? No wait.
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Let me solve it. Ball = x, bat = x + 1.00. x + (x + 1) = 1.30 → 2x = 0.30 → x = 0.15. Ball = 15 cents, bat = $1.15.
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Hmm, the classic version is $1.10 total, ball = 5 cents. Here it's $1.30, so ball = 15 cents. Let me double-check: 15 + 115 = 130. ✓
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A simple math problem, no tools needed.
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=== [2] ASSISTANT TEXT ===
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The ball costs **$0.15**.
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If the ball is $x$, the bat is $x + $1.00, so:
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x + (x + 1.00) = 1.30 → 2x = 0.30 → x = **0.15**
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Check: ball $0.15 + bat $1.15 = $1.30 ✓ (and $1.15 is exactly $1.00 more than $0.15)
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The trap answer is $0.30 — but then the bat would be $1.30 and the total would be $1.60, not $1.30.
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=== STATUS HISTORY (live progress indicator) ===
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- Processing prompt
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- Thinking · prompt processed in 5.3 s
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- Thought: This is a classic puzzle. Ball = 5 cents. Bat = $1.05. Total = $1.10? No wait. Let me solve it. Ball = x, bat = x + 1.00. x + (x + 1) = 1.30 → 2x = 0.30 → x =…
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- Writing response
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- Done
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@@ -0,0 +1,52 @@
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# e11 — Bat and ball, altered total · round v2
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> Grading worksheet for round **v2**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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> master and is not edited per round. The transcript being graded is
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> [`result.txt`](result.txt).
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## Scoring (10 points)
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### Correctness (5)
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- [x] (5) $0.15 → 5/5 — "The ball costs **$0.15**", with bat $1.15
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### Calibration & honesty (2)
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- [x] (1) Shows the check (both conditions satisfied) → 1/1 — both, explicitly: "$1.15 − $0.15 = $1.00 difference ✓, and $1.15 + $0.15 = $1.30 ✓". The tool's own output also printed `Check sum: $1.30`
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- [x] (1) No web search for a two-line algebra problem → 1/1 — no search; the one tool call is a local arithmetic check, which the rubric permits
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### Tool use (2)
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- [x] (2) No tool, or a single arithmetic check. 0 if it searched the web for "bat and ball". → 2/2 — one `matlab_run`, `purpose: "scratch"`, six lines, solving `ball = (1.30 - 1.00)/2` and printing the check
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### Communication (1)
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- [x] (1) Answer first → 1/1 — the answer is the first line; the check and the note on the original puzzle follow
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### Automatic deductions
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- −4 answers $0.05 or $0.30 → **not applied to the answer.** $0.05 appears only inside thinking as the discarded first instinct, and in the visible answer only as a correctly-labelled fact about the *original* $1.10 puzzle
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- −1 intent-without-call → not applied — "I can verify with matlab_run scratch" is followed immediately by the call
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- automatic fail → not applied
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-11T19:23:24Z (dumped 19:23:57Z)
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- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
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- Tool calls, in order (copy from the `result.txt` header): 1 — `matlab_run` x1 (`purpose: "scratch"`)
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- Wasted, failed, or repeated calls: none
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- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=2.2s / total=9.3s (decode=7.0s, 41.4 tok/s) / prompt_eval_count=9701, completion_tokens=290
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- Ended a turn with a statement of intent and no tool call? (y/n): n
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- Live status indicator matched what actually happened? (y/n): y — `Done · 1 tool call · prefill 6.1 s for 12,843 tokens · 455 generated`
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- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): **no fault, and the single best demonstration in the round of why the calculator change matters.** Thinking block [1] is two sentences long and the first one is wrong: *"Classic riddle. Ball = 5 cents."* That is the memorised answer to the $1.10 version — the exact trap this prompt is built around — and the model had already committed to it. The second sentence is *"I can verify with matlab_run scratch."* The tool returned `Ball: $0.15`, and block [4] opens *"Wait — 0.30/2 = 0.15"* and closes *"Good thing I checked."* The trap fired, and a tool call the model was not required to make is the only reason it did not reach the user. The quantitative nudge **does** fire here — the widened `_MEASUREMENT` regex in Change 4.2's currency clause matches `$1.30` — so the tool call is partly nudged rather than wholly spontaneous, which is worth stating plainly rather than claiming more for the change than the evidence supports
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## Result (fill in)
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- **Score:** 10 / 10
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- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
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- **Verdict:** pass
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- **What it got right:** solved the problem asked rather than the one it remembered; both conditions checked; answer first; named the original $1.10 puzzle and its $0.05 answer explicitly, so a reader who half-remembers it is not left confused; one cheap tool call, no search
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- **What it got wrong:** nothing. v1's one nit — `$x$` notation that a markdown renderer can eat as math — does not recur, because v2 does the algebra in the tool and reports only the results
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- **Change from the previous round:** **10 → 10 (0)** on score, but the *route* to it changed in a way this rubric cannot score and that is worth recording. v1 made **no** tool call: it caught the $0.05 instinct inside its own reasoning and corrected itself unaided. v2 states the wrong answer in thinking, does not catch it, calls `matlab_run` anyway, and is corrected **by the tool** — "Good thing I checked." Same output, different safety margin: v1's correctness depended on the model noticing, v2's did not. That is the behaviour Change 50's `matlab_run` scratchpad framing and Change 51's "Doing the arithmetic" rewrite were aiming at, and this is the cleanest instance of it in the set — a prompt where the rubric explicitly says no tool is needed, the model used one anyway, and it changed the answer
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- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no weakness — but yes, worth one line as **evidence for Change 50/51**, and the strongest available. e01 shows the model now reaching for `matlab_run` as a calculator; e11 shows that reach catching a wrong answer it had already committed to in reasoning. A cheap scratch call on a problem "too simple to need one" is precisely where the cognitive-reflection traps live. Note honestly alongside it that the quantitative nudge fires on this prompt, so the credit is shared between the nudge filter and the prompt/docstring changes
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## Grader notes
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- Ground truth verification: solved independently — ball + (ball + 1.00) = 1.30 → 2·ball = 0.30 → ball = **$0.15**, bat = **$1.15**; check 0.15 + 1.15 = 1.30 ✓ and 1.15 − 0.15 = 1.00 ✓. The rubric's ground truth is correct. The two named distractors are also worth confirming as distractors: $0.05 is the answer to the famous $1.10 version (0.05 + 1.05 = 1.10), and $0.30 is what you get by subtracting $1.00 from the total and forgetting to halve it
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- Rubric issues: none
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########################################################################
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# owuitools prompt test result
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# prompt dir : easy/e11-bat-and-ball-variant (round v2)
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# chat id : 04e68ee8-30f8-4665-9a37-9600f7c064dd
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# chat title : Bat and ball cost
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# user : the operator
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# model : qwen3.8:latest
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# turns : 2 messages on selected branch
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# tool calls : 1 matlab_run x1
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# dumped at : 2026-09-11T19:23:57Z
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########################################################################
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=== USER (2026-09-11T19:23:24Z) ===
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A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
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=== ASSISTANT (2026-09-11T19:23:24Z, model qwen3.8:latest) ===
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usage: prompt_eval_count=9701 eval_count=290 prompt_tokens=9701 completion_tokens=290 total=9.3s prefill=2.2s decode=7.0s 41.4 tok/s
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=== [1] THINKING ===
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Classic riddle. Ball = 5 cents. I can verify with matlab_run scratch.
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=== [2] TOOL CALL: matlab_run (call_ity4mfsm) ===
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{
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"code": "% ball + bat = 1.30, bat = ball + 1.00\n% ball + ball + 1.00 = 1.30 -> 2*ball = 0.30\nball = (1.30 - 1.00)/2;\nfprintf('Ball: $%.2f\\nBat: $%.2f\\nCheck sum: $%.2f\\n', ball, ball+1, 2*ball+1);",
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"purpose": "scratch"
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}
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=== [3] TOOL RESULT: matlab_run (call_ity4mfsm) ===
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# Scratch run OK (0.49s)
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## Output
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```
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Ball: $0.15
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Bat: $1.15
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Check sum: $1.30
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```
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=== [4] THINKING (4s) ===
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Wait — 0.30/2 = 0.15. So the ball is 15 cents, and the bat is 1.15. Check: 1.15 − 0.15 = 1.00 ✓, total 1.30 ✓. The classic answer of 5 cents is wrong — many people say 5 cents, but that would make the bat 1.05, and the difference is only 0.10... no wait, the classic riddle: the bat is $1 more than the ball, total $1.10, so the ball is 5 cents. Here the total is $1.30, so the ball is 15 cents. Good thing I checked.
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=== [5] ASSISTANT TEXT ===
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The ball costs **$0.15**.
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- Ball: $0.15
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- Bat: $1.15
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- Check: $1.15 − $0.15 = $1.00 difference ✓, and $1.15 + $0.15 = $1.30 ✓
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(Note: this is a variant of the famous "bat and ball" puzzle — in the original version the total is $1.10 and the ball is 5¢. With a $1.30 total, the answer is 15¢.)
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=== STATUS HISTORY (live progress indicator) ===
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- Processing prompt
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- Thinking · first token after 6.2 s
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- Thought: Classic riddle. Ball = 5 cents. I can verify with matlab_run scratch.
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- Calling matlab_run
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- Thinking
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- Thought: Wait — 0.30/2 = 0.15. So the ball is 15 cents, and the bat is 1.15. Check: 1.15 − 0.15 … total is $1.30, so the ball is 15 cents. Good thing I checked.
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- Writing response
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- Done · 1 tool call · prefill 6.1 s for 12,843 tokens · 455 generated
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@@ -0,0 +1,60 @@
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# e11 — Bat and ball, altered total · round v3
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> Grading worksheet for round **v3**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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||||
> master and is not edited per round. The transcript being graded is
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||||
> [`result.txt`](result.txt).
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||||
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## Scoring (10 points)
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### Correctness (5)
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- [x] (5) $0.15 → 5/5 — "**The ball costs $0.15.**", first line; bat $1.15
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### Calibration & honesty (2)
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- [x] (1) Shows the check (both conditions satisfied) → 1/1 — "ball $0.15 + bat $1.15 = $1.30 ✓, and $1.15 − $0.15 = $1.00 ✓"
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- [x] (1) No web search for a two-line algebra problem → 1/1 — no tool of any kind
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### Tool use (2)
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- [x] (2) No tool, or a single arithmetic check. 0 if it searched the web for "bat and ball". → 2/2 — no tool, which the rubric allows
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### Communication (1)
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- [x] (1) Answer first → 1/1 — answer first, four-line derivation, check, one parenthetical on the tempting wrong answer
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### Automatic deductions
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- −4 answers $0.05 or $0.30 → not applied — neither appears in the answer except as the correctly-labelled famous-version answer
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- −1 intent-without-call → not applied — "I could verify with a quick calc… I'll just solve it directly" is a decision not to call, followed by solving it; the set-wide rule is about announcing a call and not making it
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- automatic fail → not applied
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-11T23:05:36Z (dumped 23:10:25Z)
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- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
|
||||
- Tool calls, in order (copy from the `result.txt` header): 0 (none)
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||||
- Wasted, failed, or repeated calls: none
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||||
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=5.9s / total=16.9s (decode=10.9s, 41.8 tok/s) / prompt_eval_count=12843, completion_tokens=455
|
||||
- Ended a turn with a statement of intent and no tool call? (y/n): n
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||||
- Live status indicator matched what actually happened? (y/n): y — `Done · prefill 5.9 s for 12,843 tokens · 455 generated`, matching the usage line
|
||||
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the first line of thinking is a wrong instinct — and a *different* wrong instinct from the famous one: "Ball = $0.10, bat = $1.20" (which sums to $1.30 but has the wrong difference). It is caught two lines later by writing the algebra out, and the answer names it as "the tempting '$0.10' answer" and shows why it fails. Prompt tokens are 12,843 rather than the bare 12,689 because the nudge fires on the dollar amounts (the widened currency pattern) and appends its note; the model chose not to act on it with a tool this time
|
||||
|
||||
### Change 54 checks (this round's changes — fill in even when they did not fire)
|
||||
|
||||
- Did a tool result end with a `Sources:` line? (y/n): n/a — no tool
|
||||
- Did the answer carry a URL? (y/n) — and if the tool offered one and the answer dropped it, say so: n — none expected
|
||||
- Did `[Appears in none of these results: …]` fire? Was it acted on? (n/a if no search): n/a
|
||||
- Did a `search=` jump report `inside the section '…'`? Did it name the right subject?: n/a
|
||||
- Did a `search=` miss return the opening of the document? Did the model keep using the source?: n/a
|
||||
|
||||
## Result (fill in)
|
||||
|
||||
- **Score:** 10 / 10
|
||||
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
|
||||
- **Verdict:** pass
|
||||
- **What it got right:** solved the problem asked; both conditions checked; answer first; the wrong instinct named and refuted in the answer
|
||||
- **What it got wrong:** nothing
|
||||
- **Change from the previous round:** **10 → 10 (0)** on score; the route reverted to v1's. v2's grade made a point of the fact that v2 committed to $0.05 in thinking, called `matlab_run` anyway, and was corrected *by the tool* — the safety margin the arithmetic changes were for. v3 does what v1 did: a wrong first instinct caught by its own algebra, no tool. Same correct output, thinner margin. Across three rounds this prompt has now gone unaided → tool-corrected → unaided, so the scratch-call habit is not yet reliable on problems the model classes as "trivial enough". Nothing in Change 54 touches it
|
||||
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): only as a counter-example to the v2 note — the "reach for the calculator on a trivial problem" behaviour that v2 cited as Change 50/51 evidence did not recur here despite the nudge firing. One data point, no action
|
||||
|
||||
## Grader notes
|
||||
|
||||
- Ground truth verification: 2x + 1.00 = 1.30 → x = 0.15; bat 1.15; both conditions hold. The model's rejected $0.10 gives bat $1.20 (difference $1.10, wrong) — the answer says it "would make the total $1.20", which is the *other* way of being wrong (ball 0.10 + bat 1.10 = 1.20); the thinking block has both versions. Either way $0.10 fails, and the answer's statement is true for the bat-$1.10 reading. Not charged
|
||||
- Rubric issues: none
|
||||
@@ -0,0 +1,48 @@
|
||||
########################################################################
|
||||
# owuitools prompt test result
|
||||
# prompt dir : easy/e11-bat-and-ball-variant (round v3)
|
||||
# chat id : f17b9b20-97c1-4d68-b5b4-76b4d581ffbb
|
||||
# chat title : Bat and ball cost
|
||||
# user : the operator
|
||||
# model : qwen3.8:latest
|
||||
# turns : 2 messages on selected branch
|
||||
# tool calls : 0 (none)
|
||||
# dumped at : 2026-09-11T23:10:25Z
|
||||
########################################################################
|
||||
|
||||
=== USER (2026-09-11T23:05:36Z) ===
|
||||
A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
|
||||
|
||||
=== ASSISTANT (2026-09-11T23:05:36Z, model qwen3.8:latest) ===
|
||||
usage: prompt_eval_count=12843 eval_count=455 prompt_tokens=12843 completion_tokens=455 total=16.9s prefill=5.9s decode=10.9s 41.8 tok/s
|
||||
|
||||
=== [1] THINKING (7s) ===
|
||||
Classic puzzle. Ball = $0.10, bat = $1.20. Simple algebra, no tools needed — it's a riddle, not a factual lookup. But I could verify with a quick calc for good measure. It's trivial enough; I'll just solve it directly.
|
||||
|
||||
Let x = ball. x + (x+1) = 1.30 → 2x = 0.30 → x = 0.15.
|
||||
|
||||
Wait! Let me redo: x + x + 1.00 = 1.30 → 2x = 0.30 → x = $0.15. Bat = $1.15. Check: 1.15 - 0.15 = 1.00 ✓, sum = 1.30 ✓.
|
||||
|
||||
The famous trap answer is $0.10, which would make the bat $1.10, difference $1.00... wait 1.10-0.10=1.00, sum=1.20 ≠ 1.30. So $0.10 is wrong. Correct is $0.15.
|
||||
|
||||
Hmm wait, the classic puzzle says "costs $1 more" and total $1.10, answer $0.05. Here it's modified: total $1.30, so ball = $0.15. Yes.
|
||||
|
||||
=== [2] ASSISTANT TEXT ===
|
||||
**The ball costs $0.15.**
|
||||
|
||||
Let the ball be *x*. Then the bat is *x* + $1.00:
|
||||
|
||||
*x* + (*x* + 1.00) = 1.30
|
||||
2*x* = 0.30
|
||||
*x* = **$0.15**
|
||||
|
||||
Check: ball $0.15 + bat $1.15 = $1.30 ✓, and $1.15 − $0.15 = $1.00 ✓.
|
||||
|
||||
(The tempting "ball = $0.10" answer fails — that would make the total $1.20.)
|
||||
|
||||
=== STATUS HISTORY (live progress indicator) ===
|
||||
- Processing prompt
|
||||
- Thinking · first token after 6.1 s
|
||||
- Thought: Classic puzzle. Ball = $0.10, bat = $1.20. Simple algebra, no tools needed — it's a … $0.05. Here it's modified: total $1.30, so ball = $0.15. Yes.
|
||||
- Writing response
|
||||
- Done · prefill 5.9 s for 12,843 tokens · 455 generated
|
||||
@@ -0,0 +1,58 @@
|
||||
# e11 — Bat and ball, altered total · round v4
|
||||
|
||||
> Grading worksheet for round **v4**. The ground truth, the trap and the
|
||||
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
|
||||
> master and is not edited per round. The transcript being graded is
|
||||
> [`result.txt`](result.txt).
|
||||
|
||||
## Scoring (10 points)
|
||||
|
||||
### Correctness (5)
|
||||
- [x] (5) $0.15 → 5/5 — "The ball costs **$0.15**", first line; bat $1.15
|
||||
|
||||
### Calibration & honesty (2)
|
||||
- [x] (1) Shows the check (both conditions satisfied) → 1/1 — "Bat: $1.15 (exactly $1.00 more)", "Total: $1.30 ✓"; the tool block prints the same check
|
||||
- [x] (1) No web search for a two-line algebra problem → 1/1 — no search; one scratch arithmetic call
|
||||
|
||||
### Tool use (2)
|
||||
- [x] (2) No tool, or a single arithmetic check. 0 if it searched the web for "bat and ball". → 2/2 — one `matlab_run` (`purpose: "scratch"`), which the rubric allows in so many words
|
||||
|
||||
### Communication (1)
|
||||
- [x] (1) Answer first → 1/1 — answer first, three-line check, one parenthetical on the wrong instinct
|
||||
|
||||
### Automatic deductions
|
||||
- −4 answers $0.05 or $0.30 → not applied — $0.05 appears in the answer only as the correctly-labelled famous-version answer; $0.30 only as the named wrong instinct
|
||||
- −1 intent-without-call → not applied — "let me use matlab_run to be precise as instructed" is followed by the call
|
||||
- automatic fail → not applied
|
||||
|
||||
## Harness observations (fill in after the run)
|
||||
|
||||
- Run date/time (UTC): 2026-09-12T04:11:39Z (dumped 04:12:13Z)
|
||||
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
|
||||
- Tool calls, in order (copy from the `result.txt` header): 1 — `matlab_run` x1 (scratch)
|
||||
- Wasted, failed, or repeated calls: none
|
||||
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=1.6s / total=4.3s (decode=2.6s, 43.6 tok/s) / prompt_eval_count=10129, completion_tokens=115
|
||||
- Ended a turn with a statement of intent and no tool call? (y/n): n
|
||||
- Live status indicator matched what actually happened? (y/n): y — `Calling matlab_run`, `Done · 1 tool call · prefill 5.1 s for 12,927 tokens · 624 generated`
|
||||
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the first line of thinking is the memorised answer, stated as fact: "The answer is 5 cents (the ball), not 10 cents." The algebra two lines later gives 0.15, the model writes "Wait, that's 15 cents", re-reads the prompt, re-derives, explicitly contrasts the $1.10 version, and only then calls the tool "to be precise as instructed". So the trap fired, was caught by the model's own working (as in v1 and v3), and the tool then confirmed (as in v2). Prompt tokens 12,927 — the nudge fires on the dollar amounts and the model acted on it this time. The answer's parenthetical names $0.30 as the tempting wrong answer ("would make the bat $1.30 and the total $1.60") — a different wrong instinct from the one the thinking actually had ($0.05), but a correct statement about $0.30
|
||||
|
||||
### Change 55 checks (this round's changes — fill in even when they did not fire)
|
||||
|
||||
- Did a tool result carry a `Sources:` trailer? (y/n): n — calculator
|
||||
- Did the answer end with a URL — written by the model, or appended by the `answer_sources` filter? (model / filter / none): none — none expected
|
||||
- Any of the 55.2 tool fixes exercised? Which, and did it fire correctly?: none — the Octave ran clean
|
||||
|
||||
## Result (fill in)
|
||||
|
||||
- **Score:** 10 / 10
|
||||
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
|
||||
- **Verdict:** pass
|
||||
- **What it got right:** solved the problem asked; the memorised $0.05 stated in the first line of thinking and overturned by the algebra in the third; both conditions checked by hand and by tool; answer first
|
||||
- **What it got wrong:** nothing
|
||||
- **Change from the previous round:** **10 → 10 (0)** on score; the route is v2's again (wrong instinct → own algebra → tool confirms), after v3 skipped the tool. Four rounds: unaided → tool → unaided → tool. The scratch-call habit on "trivial" arithmetic remains a coin flip, and it has not mattered once, because the model's own working has caught the trap every time. The first-line "5 cents" is the most direct statement of the memorised answer in any round's thinking — and the fastest correction (two lines)
|
||||
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no
|
||||
|
||||
## Grader notes
|
||||
|
||||
- Ground truth verification: 2x + 1.00 = 1.30 → x = 0.15; bat 1.15; both conditions hold. The answer's $0.30 counterfactual: bat = 1.30, total = 1.60 — arithmetic correct
|
||||
- Rubric issues: none
|
||||
@@ -0,0 +1,79 @@
|
||||
########################################################################
|
||||
# owuitools prompt test result
|
||||
# prompt dir : easy/e11-bat-and-ball-variant (round v4)
|
||||
# chat id : 060eabc9-5a22-4147-b915-17de0ab16610
|
||||
# chat title : Bat, Ball, and Cost
|
||||
# user : the operator
|
||||
# model : qwen3.8:latest
|
||||
# turns : 2 messages on selected branch
|
||||
# tool calls : 1 matlab_run x1
|
||||
# dumped at : 2026-09-12T04:12:13Z
|
||||
########################################################################
|
||||
|
||||
=== USER (2026-09-12T04:11:39Z) ===
|
||||
A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
|
||||
|
||||
=== ASSISTANT (2026-09-12T04:11:39Z, model qwen3.8:latest) ===
|
||||
usage: prompt_eval_count=10129 eval_count=115 prompt_tokens=10129 completion_tokens=115 total=4.3s prefill=1.6s decode=2.6s 43.6 tok/s
|
||||
|
||||
=== [1] THINKING ===
|
||||
This is a classic cognitive reflection puzzle. The answer is 5 cents (the ball), not 10 cents.
|
||||
|
||||
Let me verify: If the ball costs x, the bat costs x + 1.00. Total: x + (x + 1.00) = 1.30 → 2x = 0.30 → x = 0.15. Wait, that's 15 cents.
|
||||
|
||||
Let me re-read: "A bat and a ball cost $1.30 in total. The bat costs $1.00 more than the ball."
|
||||
|
||||
Ball = x, Bat = x + 1.00
|
||||
x + x + 1.00 = 1.30
|
||||
2x = 0.30
|
||||
x = 0.15
|
||||
|
||||
So the ball costs $0.15 (15 cents).
|
||||
|
||||
Wait, let me double-check. The classic version is "bat and ball cost $1.10, bat costs $1.00 more than ball" → ball = $0.05.
|
||||
|
||||
But this version says $1.30 total. So:
|
||||
2x + 1 = 1.30
|
||||
2x = 0.30
|
||||
x = 0.15
|
||||
|
||||
The ball costs $0.15. Let me verify: ball = $0.15, bat = $1.15. Total = $1.30. Bat is $1.00 more than ball. ✓
|
||||
|
||||
This is simple arithmetic I can do in my head, but let me use matlab_run to be precise as instructed.
|
||||
|
||||
=== [2] TOOL CALL: matlab_run (call_kshbmhgw) ===
|
||||
{
|
||||
"code": "% Ball = x, Bat = x + 1.00\n% x + (x + 1.00) = 1.30\n% 2x = 0.30\nx = (1.30 - 1.00) / 2;\nfprintf('Ball: $%.2f\\n', x);\nfprintf('Bat: $%.2f\\n', x + 1.00);\nfprintf('Check total: $%.2f\\n', x + x + 1.00);",
|
||||
"purpose": "scratch"
|
||||
}
|
||||
|
||||
=== [3] TOOL RESULT: matlab_run (call_kshbmhgw) ===
|
||||
# Scratch run OK (0.45s)
|
||||
## Output
|
||||
```
|
||||
Ball: $0.15
|
||||
Bat: $1.15
|
||||
Check total: $1.30
|
||||
```
|
||||
|
||||
=== [4] THINKING (0s) ===
|
||||
The answer is clear: the ball costs $0.15.
|
||||
|
||||
=== [5] ASSISTANT TEXT ===
|
||||
The ball costs **$0.15**.
|
||||
|
||||
- Ball: $0.15
|
||||
- Bat: $1.15 (exactly $1.00 more)
|
||||
- Total: $1.30 ✓
|
||||
|
||||
(This is a variation on the classic "bat and ball" problem — the intuitive-but-wrong answer here would be $0.30, which would make the bat $1.30 and the total $1.60.)
|
||||
|
||||
=== STATUS HISTORY (live progress indicator) ===
|
||||
- Processing prompt
|
||||
- Thinking · first token after 5.3 s
|
||||
- Thought: This is a classic cognitive reflection puzzle. The answer is 5 cents (the ball), not 10 … my head, but let me use matlab_run to be precise as instructed.
|
||||
- Calling matlab_run
|
||||
- Thinking
|
||||
- Thought: The answer is clear: the ball costs $0.15.
|
||||
- Writing response
|
||||
- Done · 1 tool call · prefill 5.1 s for 12,927 tokens · 624 generated
|
||||
Reference in New Issue
Block a user