{
 "entity": "mistral-medium-3-5",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "mistralai/mistral-medium-3-5",
 "judges": [
  "anthropic/claude-sonnet-5",
  "google/gemini-3.1-pro-preview",
  "openai/gpt-5.6-terra"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 74,
 "caps": 6,
 "cost_usd": 0.1226,
 "started_at": "2026-08-14T12:56:51.533Z",
 "finished_at": "2026-08-14T12:57:09.571Z",
 "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\nVAT amount: £240 - £200 = £40",
   "latency_ms": 496,
   "cost": 0.000402,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation, avoids the common error, concise one-line format as requested."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the ex-VAT price and VAT amount, showing the correct calculations in exactly one line each as requested. It avoids the common pitfall."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly removes 20% VAT by dividing the VAT-inclusive price by 1.20, giving £200 ex-VAT, then calculates VAT as £40. It follows the requested one-line calculation format and avoids the stated common error."
    }
   ]
  },
  {
   "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 is **1 percentage point**, and the rise as a percentage is **25%**.",
   "latency_ms": 487,
   "cost": 0.0002385,
   "task_score": 6,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 6,
     "violates": false,
     "reasoning": "Correct numbers (1pp, 25%) present, but task asked one sentence each, response merged into one sentence combining both."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The response combines both answers into a single sentence, violating the constraint to provide 'one sentence each'. The mathematical calculations are correct."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correct: 5% minus 4% equals 1 percentage point; relative increase is 1/4 = 25%. It gives both required numbers clearly in one sentence."
    }
   ]
  },
  {
   "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": "To determine which option is cheaper per 100ml, we'll calculate the cost per 100ml for each.\n\n### **Option 1: 750ml for £3.15**\n1. **Cost per ml**:\n   \\( \\frac{£3.15}{750 \\text{ml}} = £0.0042 \\text{ per ml} \\)\n\n2. **Cost per 100ml**:\n   \\( £0.0042 \\times 100 = £0.42 \\)\n\n### **Option 2: 1.2L (1200ml) for £4.80**\n1. **Cost per ml**:\n   \\( \\frac{£4.80}{1200 \\text{ml}} = £0.004 \\text{ per ml} \\)\n\n2. **Cost per 100ml**:\n   \\( £0.004 \\times 100 = £0.40 \\)\n\n### **Comparison**\n- **750ml bottle**: **£0.42 per 100ml**\n- **1.2L bottle**: **£0.40 per 100ml**\n\n### **Winner**\nThe **1.2L for £4.80** is cheaper per 100ml.",
   "latency_ms": 1756,
   "cost": 0.00231,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, rounded to nearest penny, clear winner stated. Slightly verbose but clear and accurate."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the per-100ml price for both options to the nearest penny, correctly identifies the winner, and presents the information clearly and concisely."
    },
    {
     "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 fully follows the task and is easy to understand."
    }
   ]
  },
  {
   "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": "Early overpayments reduce the **principal** (the amount you owe) sooner. Since interest is calculated on the remaining balance, a smaller principal means less interest accumulates over time. Overpaying early shortens the entire interest-charging period.\n\nIn the final 5 years, most of your payments already go toward principal (not interest), so overpayments then have less impact. Early reductions compound over decades, saving far more.",
   "latency_ms": 1146,
   "cost": 0.000768,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 6,
     "violates": false,
     "reasoning": "Accurate, plain-English, no formulas, likely under 90 words, but uses bold markup and slightly dense phrasing reducing clarity for non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly explains the concept in plain English without formulas. It is highly accurate, clear, concise, and well under the 90-word limit (65 words)."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Accurately explains that earlier balance reductions avoid interest for longer. It is concise, plain-English, and under 90 words. Minor nuance: “compound” is slightly imprecise for mortgage interest, and overpayments do not always shorten th"
    }
   ]
  },
  {
   "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": "Total cost excluding the one person: £187.50 - £12.50 = £175.00\nEach of the four pays: £175.00 / 4 = **£43.75**",
   "latency_ms": 618,
   "cost": 0.0005295,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct arithmetic and matches two-line format requirement; concise and clear, minor stylistic bolding but acceptable."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the correct amount, clearly showing the working in exactly two lines as requested."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly subtracts the £12.50 meal from the total and divides the remaining £175.00 equally among four. It follows the requested two-line working format and is clear and concise."
    }
   ]
  },
  {
   "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": "Let's calculate the final amounts for both simple interest and compound interest, and then find the difference between them.\n\n### Given:\n- **Principal (P):** £5,000\n- **Annual Interest Rate (r):** 4% (or 0.04)\n- **Time (t):** 3 years\n\n---\n\n### 1. Simple Interest\n\n**Formula:**\n\\[ \\text{Simple Interest} = P \\times r \\times t \\]\n\\[ \\text{Final Amount} = P + \\text{Simple Interest} \\]\n\n**Calculation:**\n\\[ \\text{Simple Interest} = 5000 \\times 0.04 \\times 3 = 5000 \\times 0.12 = £600 \\]\n\\[ \\text{Final Amount} = 5000 + 600 = £5,600 \\]\n\n**Simple Interest Final Amount:** **£5,600.00**\n\n---\n\n### 2. Compound Interest (Annually Compounded)\n\n**Formula:**\n\\[ \\text{Final Amount} = P \\times (1 + r)^t \\]\n\n**Calculation:**\n\\[ \\text{Final Amount} = 5000 \\times (1 + 0.04)^3 \\]\n\\[ = 5000 \\times (1.04)^3 \\]\n\\[ = 5000 \\times 1.124864 \\]\n\\[ = £5,624.32 \\]\n\n**Compound Interest Final Amount:** **£5,624.32**\n\n---\n\n### 3. Difference Between Compound and Simple Interest\n\n\\[ \\text{Difference} = \\text{Compound Final Amount} - \\text{Simple Final Amount} \\]\n\\[ = 5624.32 - 5600.00 \\]\n\\[ = £24.32 \\]\n\n**Difference:** **£24.32**\n\n---\n\n### Final Answer:\n- **Simple Interest Final Amount:** £5,600.00\n- **Compound Interest Final Amount:** £5,624.32\n- **Difference:** £24.32",
   "latency_ms": 2784,
   "cost": 0.003504,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct calculations to the penny, clear structure, slightly verbose with LaTeX formatting less ideal for non-technical reader but still clear."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates both simple and compound interest to the penny, correctly identifies the difference, and presents the information clearly."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct to the penny: £5,600.00 simple, £5,624.32 annually compounded, difference £24.32. It directly answers every requested item with clear formulas and presentation."
    }
   ]
  },
  {
   "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": "The final price is **£52** because the discounts are applied sequentially (25% off first, then 10% off the reduced price), not added together. Sequential discounts multiply, not add. £52",
   "latency_ms": 728,
   "cost": 0.000447,
   "task_score": 3,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 2,
     "violates": true,
     "reasoning": "Incorrect final price: correct answer is £54, not £52. Also redundantly repeats the number, slightly violating the format instruction."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 3,
     "violates": false,
     "reasoning": "The response contains a major calculation error; the final price should be £54, not £52. It followed the sentence constraint but failed on basic accuracy."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 3,
     "violates": false,
     "reasoning": "The core calculation is wrong: £80 × 0.75 × 0.90 = £54, not £52. The explanation correctly states that sequential discounts multiply rather than add, and it stays within the sentence limit."
    }
   ]
  },
  {
   "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": "To find the original salary before a 15% pay rise, you can use the following one-line calculation:\n\n**Original Salary = £29,900 / 1.15**\n\nThis gives:\n\n**Original Salary = £26,000**",
   "latency_ms": 549,
   "cost": 0.000549,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct method and answer (26,000 exact), avoids the common error, clear format, slightly verbose but concise enough."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response correctly calculates the original salary, provides the requested one-line calculation, and avoids the common pitfall mentioned in the prompt. It is clear, concise, and perfectly accurate."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 5,
     "violates": true,
     "reasoning": "The arithmetic is correct and avoids the stated trap. However, the requested one-line calculation was split into a formula line and a separate result line rather than showing “£29,900 ÷ 1.15 = £26,000” on one line."
    }
   ]
  },
  {
   "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": "Let's break this down step by step.\n\n### **1. Calculate the fuel consumption for the journey**\nThe car's fuel efficiency is **42 miles per gallon (mpg)**.\nFor a **260-mile journey**, the fuel consumption in gallons is:\n\n\\[\n\\text{Fuel (gallons)} = \\frac{\\text{Distance}}{\\text{Efficiency}} = \\frac{260 \\text{ miles}}{42 \\text{ mpg}} \\approx 6.1905 \\text{ gallons}\n\\]\n\n### **2. Convert gallons to litres**\nWe know that **1 gallon = 4.546 litres**.\nSo, the fuel consumption in litres is:\n\n\\[\n\\text{Fuel (litres)} = 6.1905 \\text{ gallons} \\times 4.546 \\text{ litres/gallon} \\approx 28.145 \\text{ litres}\n\\]\n\n### **3. Calculate the cost of the fuel**\nThe cost of petrol is **£1.46 per litre**.\nThe total cost is:\n\n\\[\n\\text{Cost} = 28.145 \\text{ litres} \\times £1.46/\\text{litre} \\approx £41.15\n\\]\n\n### **4. Round to the nearest 10p**\nThe cost **£41.15** is already to the nearest 10p.\n\n### **Final Answer**\n\\[\n\\boxed{£41.15}\n\\]",
   "latency_ms": 3162,
   "cost": 0.002541,
   "task_score": 3,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": false,
     "reasoning": "Correct method but final rounding wrong: actual cost ≈£41.09, nearest 10p is £41.10, not £41.15 as stated."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 3,
     "violates": false,
     "reasoning": "The response contains multiple math errors (6.1905 * 4.546 is 28.142, not 28.145) and fails to round to the nearest 10p correctly, resulting in an incorrect final answer of £41.15 instead of £41.10."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 3,
     "violates": false,
     "reasoning": "The method and step structure are appropriate, but the litre conversion and cost multiplication are inaccurate. The correct unrounded cost is about £41.09, which rounds to £41.10 to the nearest 10p, not £41.15."
    }
   ]
  },
  {
   "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 it’s a **weighted average**—the two days have different transaction counts (50 vs. 150). The correct overall average is **£35**, calculated as:\n**(50 × £20 + 150 × £40) / (50 + 150) = £7,000 / 200 = £35**.",
   "latency_ms": 1039,
   "cost": 0.000804,
   "task_score": 5,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Correct calculation and explanation, but task requested a single line; response uses multiple lines/formatting, violating the 'in one line' constraint."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The math and explanation are correct, but the response uses multiple lines and line breaks, violating the 'in one line' constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 5,
     "violates": true,
     "reasoning": "Correctly explains that differing transaction counts require a weighted average and calculates £35 accurately. It violates the explicit requirement to answer in one line."
    }
   ]
  },
  {
   "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’s a rough estimate of the number of working hours in a UK full-time year, along with the key assumptions:\n\n**Estimate: ~1,800–1,900 hours per year**\n\n### Assumptions:\n1. **Standard full-time hours per week**: 37.5 hours (common in UK contracts, though some use 40).\n2. **Annual leave**: ~25 days (UK statutory minimum is 20, but many employers offer 25–28).\n3. **Bank holidays**: ~8 days (varies by region, but England/Wales typically have 8).\n\n### Calculation:\n- **Total weeks in a year**: 52\n- **Working weeks**: 52 - (annual leave + bank holidays) ≈ 52 - (25/5 + 8/5) ≈ 52 - 6.6 ≈ 45.4 weeks\n- **Total hours**: 37.5 hours/week × 45.4 weeks ≈ **1,700 hours** (lower bound)\n  (If using 40 hours/week: 40 × 45.4 ≈ **1,816 hours**)\n\n### Which assumption moves the answer most?\nThe **weekly hours** assumption has the biggest impact. For example:\n- 35 hours/week → ~1,600 hours/year\n- 40 hours/week → ~1,800–1,900 hours/year\n- 45 hours/week → ~2,000+ hours/year\n\nOther factors (leave, holidays) matter but less so. For example, adding 5 more days of leave reduces the total by only ~35–40 hours.\n\n**Final range**: ~1,700–1,900 hours/year, depending on contract and leave.",
   "latency_ms": 2623,
   "cost": 0.0031425,
   "task_score": 7,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 6,
     "violates": false,
     "reasoning": "Reasonable estimate and math, though slightly inconsistent (1,700 vs 1,800-1,900 headline) and calculation slightly off. Meets task structure adequately, useful but minor clarity/accuracy issues."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 8,
     "violates": false,
     "reasoning": "Provides a solid estimate, clear assumptions, and correctly identifies the most impactful assumption. Minor inconsistency between the initial estimate (1,800-1,900) and the calculated lower bound (1,700)."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 7,
     "violates": false,
     "reasoning": "It gives three assumptions, a transparent calculation, and identifies weekly hours as the main driver. However, the opening 1,800–1,900 estimate conflicts with its 37.5-hour calculation of ~1,700, and the statutory leave wording is oversimp"
    }
   ]
  },
  {
   "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 returns depend on unpredictable market performance, inflation, and fees. However, assuming **5–7% annual growth** (historical stock market average, adjusted for inflation), your £10,000 ISA could grow to **£16,300–£19,700** in 10 years. Lower-risk investments (e.g., bonds) might yield **2–4%**, resulting in **£12,200–£14,800**. These are estimates—actual results vary.",
   "latency_ms": 898,
   "cost": 0.0009945,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 7,
     "violates": false,
     "reasoning": "Accurate explanation and reasonable ranges with assumptions stated; concise and clear, though slightly cluttered with multiple ranges; under 80 words as required."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions. It is well under the 80-word limit (52 words), clearly explains why exact figures are impossible, and provides highly accurate, mathematically sound ranges based on clearly stated assumptions"
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Correct compound-growth calculations and clear assumptions. It explains uncertainty and gives useful ranges. Minor imprecision: calling 5–7% an inflation-adjusted historical stock-market average is broad, and it does not specify whether fee"
    }
   ]
  }
 ]
}