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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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