{
 "entity": "gemini-3-1-pro",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "google/gemini-3.1-pro-preview",
 "judges": [
  "anthropic/claude-sonnet-5",
  "openai/gpt-5.6-terra",
  "x-ai/grok-4.5"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 96,
 "caps": 1,
 "cost_usd": 0.2128,
 "started_at": "2026-08-14T12:53:41.068Z",
 "finished_at": "2026-08-14T12:54:28.462Z",
 "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**VAT amount:** £240 - £200 = £40",
   "latency_ms": 6123,
   "cost": 0.00896,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, avoids the common error, follows one-line-each format, clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly removes VAT by dividing the VAT-inclusive price by 1.20, giving £200 ex-VAT, then calculates £40 VAT. Provides one clear calculation line for each requested value."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct ex-VAT and VAT calc shown one line each; avoids common error; clear, concise, fully follows task."
    }
   ]
  },
  {
   "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 rise in percentage points is 1. \nThe rise as a percentage is 25%.",
   "latency_ms": 6572,
   "cost": 0.010206,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 7,
     "violates": false,
     "reasoning": "Correct values (1 pp, 25%), both present, concise, but format is two lines rather than clearly labeled sentences; minor phrasing awkwardness."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Correctly gives a 1 percentage-point increase and a 25% relative increase in two concise sentences. The first answer would be clearer as “1 percentage point” rather than simply “1,” but the intended value is unambiguous."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math and dual one-sentence format; both required numbers present. Minor polish only (units implied)."
    }
   ]
  },
  {
   "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": "Here is the breakdown of the price per 100ml for each option:\n\n*   **750ml for £3.15:** \n    £3.15 ÷ 7.5 (since there are 7.5 lots of 100ml in 750ml) = **£0.42** (42p per 100ml)\n\n*   **1.2L (1200ml) for £4.80:** \n    £4.80 ÷ 12 (since there are 12 lots of 100ml in 1200ml) = **£0.40** (40p per 100ml)\n\n**The Winner:**\nThe **1.2L for £4.80** is the cheaper option.",
   "latency_ms": 6373,
   "cost": 0.01109,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear per-100ml prices, correct winner, concise and well-formatted."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both unit-price calculations are correct, rounded to the nearest penny, and the cheaper 1.2L option is clearly identified. The response is concise, clear, and directly addresses every requirement."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct prices to nearest penny; clear winner named; fully follows task; concise and useful."
    }
   ]
  },
  {
   "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 your outstanding balance. When you overpay £100 early on, you immediately shrink that balance, meaning you avoid paying interest on that £100 for the remaining 20+ years of the loan. \n\nIf you wait until the final five years to overpay, that same £100 only prevents a few years' worth of interest. Early overpayments give your money decades to work for you, stripping away future interest charges long before they can accumulate.",
   "latency_ms": 7391,
   "cost": 0.01011,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, plain English, no formulas. Slightly under length check needed—about 85 words, within limit. Minor redundancy but effective and useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurately explains that early overpayments reduce the balance for far longer, preventing more future interest. Plain English, no formulas, directly compares early versus final-five-year payments, and stays well under 90 words."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate plain-English reason, 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 (total) - £12.50 (one person's share) = £175.00 remaining\n£175.00 ÷ 4 people = £43.75 each",
   "latency_ms": 4440,
   "cost": 0.006102,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, clear two-line working as requested, concise and useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly subtracts the £12.50 meal-only share from the total, then divides the remaining £175 equally among four people. It follows the requested two-line working format and is clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact arithmetic and two-line working as required; fully correct, 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": "Here are the calculations for your £5,000 investment over 3 years at a 4% annual interest rate:\n\n**1. Simple Interest**\n*   **Calculation:** £5,000 × 4% × 3 years = £600 in interest.\n*   **Final Amount:** **£5,600.00**\n\n**2. Annual Compound Interest**\n*   **Calculation:** £5,000 × (1.04)³ = £5,624.32\n*   **Final Amount:** **£5,624.32**\n\n**The Difference**\n*   **Calculation:** £5,624.32 - £5,600.00\n*   **Difference:** **£24.32** \n\n*(Compound interest yields £24.32 more over the 3 years because you are earning interest on your previously accumulated interest).*",
   "latency_ms": 8789,
   "cost": 0.013244,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, penny precision, clear structure, meets all task requirements concisely and accurately."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct to the penny: simple £5,600.00, annual compounding £5,624.32, difference £24.32. It directly answers every requested item clearly and concisely."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct figures to the penny for simple, compound and difference; clear, complete and fully compliant."
    }
   ]
  },
  {
   "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\nIt is not 35% off because the second discount of 10% is applied to the already reduced price of £60, rather than the original £80. This means you are taking 10% off a smaller number, resulting in an actual total discount of 32.5%.",
   "latency_ms": 9878,
   "cost": 0.015468,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Correct math (£54, 32.5% actual discount), but response has 3 sentences plus number, exceeding stated two-sentence max."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correct final price and explanation: discounts compound (£80 × 75% × 90% = £54), producing a 32.5% total discount. It uses two explanatory sentences plus the number."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc (£54), clear explanation of sequential discounts, exactly two sentences plus number."
    }
   ]
  },
  {
   "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": 5119,
   "cost": 0.00705,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (29900/1.15=26000), one-line format as requested, avoids common error."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly reverses the 15% increase by dividing £29,900 by 1.15, giving £26,000. It provides the requested one-line calculation and avoids the stated common error."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc avoiding common error; exactly one-line as required; clear and fully useful."
    }
   ]
  },
  {
   "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": "Here is the step-by-step calculation for the cost of the journey:\n\n**Step 1: Calculate how many gallons are needed for the journey**\nTo find out how many gallons the car will use, divide the total distance by the miles per gallon (mpg).\n* 260 miles ÷ 42 mpg = **6.19047... gallons** \n*(Note: We will keep the long decimal for the next steps to ensure accuracy).*\n\n**Step 2: Convert the gallons into litres**\nSince the fuel is priced in litres, we need to multiply the number of gallons by the conversion rate (1 gallon = 4.546 litres).\n* 6.19047... gallons × 4.546 litres/gallon = **28.1419... litres**\n\n**Step 3: Calculate the total cost of the fuel**\nMultiply the total number of litres by the price per litre (£1.46).\n* 28.1419... litres × £1.46 = **£41.08718...**\n\n**Step 4: Round to the nearest 10p**\nThe total cost is £41.08 (and a bit). Because 8p is closer to 10p than it is to 0p, we round up to the nearest 10 pence.\n* £41.087... rounded to the nearest 10p is **£41.10**\n\nThe 260-mile journey will cost **£41.10** in fuel.",
   "latency_ms": 9251,
   "cost": 0.014442,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, clear steps, accurate rounding logic, meets task requirements concisely."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct, units are handled properly, and the final £41.10 is correctly rounded to the nearest 10p. It clearly shows each required step and is concise and useful."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc and rounding; clear steps; fully follows task; highly 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 transactions on Tuesday, which weights the true average closer to £40, making it exactly £35.",
   "latency_ms": 5745,
   "cost": 0.007534,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (£35), clear one-line explanation of weighting, concise and accurate."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly explains that unequal transaction counts require a weighted average and gives the correct result: (£20×50 + £40×150) ÷ 200 = £35. It is concise and presented in one line."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted average explanation and value of £35; single concise line fully answers the query."
    }
   ]
  },
  {
   "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": "Here is the estimate, the underlying assumptions, and the sensitivity of those assumptions.\n\n**The Estimate**\nThere are roughly **1,740 actual working hours** in a UK full-time year. \n\n*(Note: If you are looking for total **contracted/paid hours** before holidays are deducted—which HR departments use to calculate hourly pay from a salary—the number is roughly **1,950 hours**).*\n\n**The 3 Assumptions**\nThis estimate rests on the following three assumptions:\n\n1. **Weekly Working Hours:** I am assuming a standard UK full-time contract of **37.5 hours per week**. (This typically represents working 9:00 am to 5:30 pm, Monday to Friday, with a one-hour unpaid lunch break). \n2. **Annual Leave & Bank Holidays:** I am assuming the worker takes the exact UK statutory minimum for paid time off, which is **28 days (5.6 weeks)** per year. This figure includes the 8 standard UK bank holidays. \n3. **Weeks in a Year:** I am assuming exactly **52 weeks** in a year for mathematical simplicity. \n\n*The Calculation: 52 weeks minus 5.6 weeks of holiday leaves 46.4 actual working weeks. 46.4 weeks × 37.5 hours = 1,740 hours.*\n\n**Which assumption moves the answer most?**\n**Assumption 1 (Weekly Working Hours)** moves the answer by far the most. \n\nHere is why:\n* **Changing the weekly hours:** UK full-time contracts vary widely, most commonly sitting anywhere between 35 and 40 hours. If someone works a 40-hour week instead of a 35-hour week, that 5-hour difference across 46.4 working weeks changes the annual total by **232 hours**.\n* **Changing the holiday allowance:** If a worker has a generous holiday package (e.g., 33 days off instead of the statutory 28), those extra 5 days off only reduce the annual total by **37.5 hours**.\n* **Changing the weeks in a year:** If we use the exact astronomical calendar (52.14 weeks instead of 52), it only adds about **5 hours** to the year. \n\nTherefore, the specific hours dictated by an individual's employment contract is the single biggest variable in this estimate.",
   "latency_ms": 15805,
   "cost": 0.023792,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, well-structured, clear calculation and sensitivity analysis; slightly verbose but appropriate for a non-technical professional."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate calculation and sensible UK assumptions: 37.5 hours/week, 28 statutory leave days including bank holidays, and 52 weeks. It clearly identifies weekly contracted hours as the largest practical driver. Minor caveat: holiday arrangeme"
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate estimate and calc; clear assumptions with sensitivity analysis; fully addresses task usefully and concisely."
    }
   ]
  },
  {
   "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 market returns and interest rates are entirely unpredictable. \n\nHowever, we can project a defensible range. Assuming an average annual growth rate of 4% (typical for a competitive Cash ISA) to 7% (historical average for a Stocks & Shares ISA), your £10,000 would grow to between **£14,800 and £19,670** in 10 years. \n\nKeep in mind that inflation will reduce this money's real-world purchasing power.",
   "latency_ms": 8080,
   "cost": 0.012608,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, meets word limit reasonably (~70 words), provides range and assumptions, useful and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Meets the word limit, explains uncertainty, states assumptions, and calculations are correct. Minor overstatement: interest rates are not always entirely unpredictable, especially for fixed-rate Cash ISAs; the assumed Cash ISA rate may not "
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate explanation and compound growth range with stated assumptions; under 80 words; clear, useful, minor polish only."
    }
   ]
  }
 ]
}