{
 "entity": "gpt-5-6-sol",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "openai/gpt-5.6-sol",
 "judges": [
  "anthropic/claude-sonnet-5",
  "google/gemini-3.1-pro-preview",
  "x-ai/grok-4.5"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 99,
 "caps": 0,
 "cost_usd": 0.1572,
 "started_at": "2026-08-14T12:52:22.478Z",
 "finished_at": "2026-08-14T12:52:56.093Z",
 "tasks": [
  {
   "id": "ma1",
   "name": "VAT both ways",
   "prompt": "A price is £240 including 20% VAT. What is the ex-VAT price, and what is the VAT amount? Show the calculation in one line each. The common wrong answer subtracts 20% of £240 — do not make it.",
   "output": "Ex-VAT price: £240 ÷ 1.20 = **£200**\n\nVAT amount: £240 − £200 = **£40**",
   "latency_ms": 1324,
   "cost": 0.00134,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, avoids common error, concise one-line format as requested, clear and useful."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response correctly calculates the ex-VAT price and VAT amount, showing the calculations in exactly one line each as requested, and avoids the common mistake."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and results; one-line each as required; avoids common error; clear and concise for non-experts."
    }
   ]
  },
  {
   "id": "ma2",
   "name": "Percentage change vs points",
   "prompt": "An interest rate rises from 4% to 5%. In one sentence each: what is the rise in percentage points, and what is the rise as a percentage? Both numbers must appear.",
   "output": "The interest rate rises by 1 percentage point.  \nThe interest rate rises by 25% relative to its original value.",
   "latency_ms": 1393,
   "cost": 0.001095,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct: 1 percentage point and 25% both stated accurately, concise, follows two-sentence format."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates both values, includes both numbers, and perfectly follows the constraint of using exactly one sentence for each explanation."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct 1 pp and 25% rises; two clear one-sentence answers; both numbers present; fully meets task."
    }
   ]
  },
  {
   "id": "ma3",
   "name": "Unit price comparison",
   "prompt": "Which is cheaper per 100ml: 750ml for £3.15, or 1.2L for £4.80? Show the per-100ml price of each to the nearest penny and name the winner.",
   "output": "- **750ml for £3.15:** **£0.42 per 100ml**\n- **1.2L for £4.80:** **£0.40 per 100ml**\n\n**Winner: 1.2L for £4.80**, cheaper by **2p per 100ml**.",
   "latency_ms": 5113,
   "cost": 0.003415,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculations, per-100ml prices accurate, winner identified clearly, concise and well-formatted."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates both prices per 100ml to the nearest penny, correctly identifies the cheaper option, and presents the information clearly and concisely."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct prices and winner; fully follows task; clear and concise."
    }
   ]
  },
  {
   "id": "ma4",
   "name": "Mortgage overpayment intuition",
   "prompt": "In under 90 words, explain why overpaying £100/month early in a 25-year mortgage saves more interest than the same overpayments in the final 5 years. No formulas — the reason, in plain English.",
   "output": "Mortgage interest is charged on the amount you still owe. Overpaying early reduces that balance for many years, so you avoid interest on the overpaid amount throughout most of the mortgage. It also means more of each later payment goes toward clearing the remaining debt rather than interest. In the final five years, the balance is already much lower and there is little time left for interest to build up, so identical overpayments save far less.",
   "latency_ms": 5363,
   "cost": 0.00518,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, no formulas, within word limit (~78 words). Slightly repetitive but concise and useful."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response is perfectly accurate, clear, and concise. It explains the concept in plain English without formulas and strictly adheres to the word count constraint (77 words)."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate plain-English explanation of early vs late overpayments; under 90 words, no formulas; clear and useful."
    }
   ]
  },
  {
   "id": "ma5",
   "name": "Split a bill with a twist",
   "prompt": "Dinner cost £187.50 for 5 people, but one person only had a £12.50 main and drinks no alcohol; the other four agree to split the rest equally. What does each of the four pay? Show the working in two lines.",
   "output": "£187.50 − £12.50 = £175.00  \n£175.00 ÷ 4 = **£43.75 each**",
   "latency_ms": 4253,
   "cost": 0.00383,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct arithmetic, exactly two lines as requested, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, provides the correct mathematical calculation, and strictly adheres to the two-line constraint."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact two-line working, correct arithmetic, fully clear and useful."
    }
   ]
  },
  {
   "id": "ma6",
   "name": "Compound vs simple",
   "prompt": "£5,000 at 4% a year for 3 years: give the final amount under simple interest and under annual compounding, both to the penny, and the difference between them.",
   "output": "- **Simple interest:** £5,600.00  \n- **Annual compounding:** £5,624.32  \n- **Difference:** **£24.32** more with annual compounding.",
   "latency_ms": 4229,
   "cost": 0.003315,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Calculations correct: 5600.00, 5624.32, difference 24.32, all to the penny, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the simple interest, compound interest, and the difference, presenting them clearly and concisely to the penny as requested."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct figures to the penny; fully addresses all parts clearly and concisely."
    }
   ]
  },
  {
   "id": "ma7",
   "name": "The discount stack",
   "prompt": "A £80 item has '25% off' and then a further '10% off at checkout'. What is the final price, and why is it not 35% off? Two sentences maximum plus the number.",
   "output": "**£54**\n\nThe discounts apply sequentially: £80 × 75% × 90% = £54. The second 10% is taken from £60, so the total discount is 32.5%, not 35%.",
   "latency_ms": 5410,
   "cost": 0.00526,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation and explanation, format matches requested structure with number plus two sentences."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the final price, accurately explains the sequential discounting, and strictly adheres to the two-sentence maximum plus the number constraint."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct final price and explanation of sequential discounts; exactly meets two-sentence-plus-number limit; clear and useful."
    }
   ]
  },
  {
   "id": "ma8",
   "name": "Reverse percentage",
   "prompt": "After a 15% pay rise, a salary is £29,900. What was it before the rise? Show the one-line calculation. The common wrong answer takes 15% off £29,900 — do not make it.",
   "output": "£29,900 ÷ 1.15 = **£26,000**",
   "latency_ms": 1781,
   "cost": 0.0009,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation (26000×1.15=29900), one-line format as required, avoids the common wrong approach."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing the correct one-line calculation and avoiding the common mistake."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct one-line calc avoiding the common error; fully meets all task requirements with clarity."
    }
   ]
  },
  {
   "id": "ma9",
   "name": "Rate to reality",
   "prompt": "A car does 42 miles per gallon. Petrol is £1.46/litre. One gallon is 4.546 litres. What does a 260-mile journey cost in fuel, to the nearest 10p? Show each step.",
   "output": "1. **Gallons needed:**\n\n\\[\n260 \\div 42 = 6.1905 \\text{ gallons}\n\\]\n\n2. **Convert gallons to litres:**\n\n\\[\n6.1905 \\times 4.546 = 28.1419 \\text{ litres}\n\\]\n\n3. **Calculate the cost:**\n\n\\[\n28.1419 \\times £1.46 = £41.0872\n\\]\n\n4. **Round to the nearest 10p:**\n\n\\[\n\\boxed{£41.10}\n\\]",
   "latency_ms": 4758,
   "cost": 0.006995,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Calculations correct, clear steps, final answer rounded properly to £41.10. Minor rounding intermediate but final result accurate."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, accurately calculating the cost step-by-step and correctly rounding to the nearest 10p. It is clear, concise, and highly useful."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc and rounding; clear numbered steps match request; fully useful and concise."
    }
   ]
  },
  {
   "id": "ma10",
   "name": "Average of averages trap",
   "prompt": "A shop's average sale was £20 across 50 Monday transactions and £40 across 150 Tuesday transactions. In one line: why is the overall average NOT £30, and what is it?",
   "output": "The overall average is not £30 because there were three times as many Tuesday transactions; the weighted average is \\((50×£20+150×£40)/200=£35\\).",
   "latency_ms": 1879,
   "cost": 0.00152,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (1000+6000)/200=£35, concise one-line explanation matching task requirements."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows the one-line constraint, accurately explains the concept of weighted averages, and correctly calculates the overall average as £35."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted avg explanation and calc in one line; fully addresses task."
    }
   ]
  },
  {
   "id": "ma11",
   "name": "Estimate honestly",
   "prompt": "Roughly how many working hours are there in a UK full-time year? Give your estimate, show the 2-3 assumptions it rests on, and say which assumption moves the answer most.",
   "output": "**Rough estimate: about 1,740 working hours per year.**\n\nAssumptions:\n\n1. **37.5 paid working hours per week** (7.5 hours × 5 days).\n2. **52 weeks per year.**\n3. **28 days of paid leave**, including UK bank holidays—equivalent to 5.6 weeks.\n\nCalculation:\n\n\\[\n(52 - 5.6) \\times 37.5 \\approx 1,740 \\text{ hours}\n\\]\n\nThe assumption that moves the answer most is **weekly contracted hours**. A 40-hour week under the same leave assumption gives about **1,856 hours**, whereas changing annual leave by one week changes the result by only **37.5 hours**.",
   "latency_ms": 7614,
   "cost": 0.01214,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct estimate, clear assumptions, math checks out, identifies most impactful assumption. Concise and useful, minor debatable claim about which assumption moves most but reasonably justified."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing a clear estimate, exactly three well-founded assumptions, and correctly identifying the most impactful assumption with a clear explanation."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate UK estimate with clear assumptions, calc, and sensitivity; fully meets all task elements; concise and professional."
    }
   ]
  },
  {
   "id": "ma12",
   "name": "Refuse false precision",
   "prompt": "Someone asks: 'Exactly how much will my £10,000 ISA be worth in 10 years?' Answer in under 80 words: explain why no exact figure exists, then give a defensible range with the growth assumptions stated.",
   "output": "No exact figure exists because future interest rates, investment returns, fees, and inflation are unknown. Assuming no further deposits or withdrawals and average annual growth after fees of 2%–7%, compounded yearly, £10,000 would become roughly **£12,200–£19,700** after 10 years. This is illustrative, not guaranteed; an investment ISA could also fall in value.",
   "latency_ms": 10171,
   "cost": 0.008695,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate, concise, meets word limit, correctly explains uncertainty and gives defensible range with clear assumptions; minor stylistic bolding but no issues."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Meets all constraints perfectly. The word count is 54 (under 80), the math is accurate based on the stated 2-7% assumptions, and it clearly explains the uncertainty of future returns."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Meets word limit, correctly explains uncertainty, states assumptions, and gives accurate compounded range."
    }
   ]
  }
 ]
}