{
 "entity": "deepseek-v4-flash",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "deepseek/deepseek-v4-flash",
 "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": 93,
 "caps": 2,
 "cost_usd": 0.0973,
 "started_at": "2026-08-14T12:47:30.172Z",
 "finished_at": "2026-08-14T12:48:04.827Z",
 "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 ÷ 1.2 = £200  \nVAT amount: £240 − £200 = £40",
   "latency_ms": 4793,
   "cost": 0.000115253,
   "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."
    },
    {
     "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 one line each as requested, and avoids the common mistake."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly removes 20% VAT by dividing the VAT-inclusive price by 1.2, then calculates VAT as the difference. Provides exactly one calculation line for each requested amount."
    }
   ]
  },
  {
   "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 percentage point (from 4% to 5%), and the rise as a percentage is 25% (since 1 is 25% of 4).",
   "latency_ms": 1524,
   "cost": 0.00001143,
   "task_score": 5,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Correct numbers but combined into one sentence instead of two separate sentences as requested ('In one sentence each')."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The math is perfectly accurate, but the response combines both answers into a single sentence instead of providing one sentence for each as instructed."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly states a 1 percentage-point increase and a 25% relative increase. Both numbers appear, the explanation is accurate, and the single sentence clearly addresses both requested parts."
    }
   ]
  },
  {
   "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": "The 750ml bottle costs £3.15, which is £0.42 per 100ml (to the nearest penny).  \nThe 1.2L bottle costs £4.80, which is £0.40 per 100ml (to the nearest penny).  \n\nThe 1.2L for £4.80 is cheaper per 100ml.",
   "latency_ms": 4913,
   "cost": 0.00008302,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculations, per-100ml prices accurate, winner correctly identified, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the per-100ml prices, accurately identifies the cheaper option, and presents the information clearly and concisely."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both unit-price calculations are correct: £3.15/7.5 = £0.42 and £4.80/12 = £0.40 per 100ml. It rounds to nearest penny and clearly identifies the cheaper option."
    }
   ]
  },
  {
   "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 shrink the loan balance sooner, so less interest accrues on that lower amount for the entire remaining term—potentially 25 years of savings. Later overpayments only reduce interest for a few years, giving the debt far less time to compound your benefit. In short, the earlier you pay, the more future interest you avoid.",
   "latency_ms": 2292,
   "cost": 0.00005194,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, no formulas, plain English, under 90 words. Minor: could be slightly more precise but overall strong and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Perfectly explains the concept in plain English without formulas, stays well under the word limit, and is highly clear and accurate."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Accurately explains that early payments reduce the balance for longer, avoiding more future interest. Clear, concise, under 90 words, and formula-free. “Compound your benefit” is slightly imprecise for typical amortizing mortgages but does "
    }
   ]
  },
  {
   "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 minus the one person's main: £187.50 - £12.50 = £175.00  \nRemaining cost split equally among four: £175.00 ÷ 4 = £43.75 each.",
   "latency_ms": 12880,
   "cost": 0.00007652078,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct math, clear two-line working as requested, concise and useful for non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, including the two-line constraint. The math is accurate, and the explanation is clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly subtracts the £12.50 individual meal from the total and divides the £175.00 remainder equally among four. It shows clear working in exactly two lines."
    }
   ]
  },
  {
   "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:\n\n**Simple Interest**  \nFinal amount = £5,000 × (1 + 0.04 × 3) = £5,000 × 1.12 = **£5,600.00**\n\n**Annual Compounding**  \nFinal amount = £5,000 × (1.04)³ = £5,000 × 1.124864 = **£5,624.32**\n\n**Difference**  \n£5,624.32 − £5,600.00 = **£24.32**\n\n**Summary:**  \n- Simple interest: **£5,600.00**  \n- Annual compounding: **£5,624.32**  \n- Difference: **£24.32**",
   "latency_ms": 4872,
   "cost": 0.00003114,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, accurate to the penny, clear format, meets task requirements exactly."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the simple and compound interest amounts to the penny, as well as the difference, presenting them clearly and concisely."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct to the penny: simple interest is £5,600.00, annual compounding is £5,624.32, and the difference is £24.32. The response directly addresses every requested item clearly."
    }
   ]
  },
  {
   "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. The discounts are applied sequentially, so the first 25% reduces the price to £60, then 10% off that gives £54, which is a total of only 32.5% off, not 35%.",
   "latency_ms": 1202,
   "cost": 0.00002072,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math (80*0.75*0.9=54), explains sequential discounts, concise, within two sentences plus number."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response is mathematically correct, perfectly explains the sequential nature of the discounts, and strictly adheres to the length constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correct final price and explanation: 25% off £80 gives £60, then 10% off £60 gives £54. It correctly identifies the combined discount as 32.5%, uses two sentences, and is clear and concise."
    }
   ]
  },
  {
   "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": 2683,
   "cost": 0.0000469,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation, correct answer, avoids common error, concise one-line format as requested."
    },
    {
     "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 pitfall."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly reverses a 15% increase by dividing the final salary by 1.15. The calculation equals £26,000 and is presented as the requested one-line calculation."
    }
   ]
  },
  {
   "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 go step-by-step.\n\n**Step 1: Find the number of gallons needed for 260 miles.**  \nThe car does 42 miles per gallon.  \n\\[\n\\text{Gallons needed} = \\frac{260}{42}\n\\]  \n\\[\n\\frac{260}{42} = \\frac{130}{21} \\approx 6.190476 \\text{ gallons}\n\\]\n\n**Step 2: Convert gallons to litres.**  \n1 gallon = 4.546 litres.  \n\\[\n\\text{Litres needed} = 6.190476 \\times 4.546\n\\]  \nFirst, do the multiplication:  \n\\[\n6.190476 \\times 4.546 \\approx 6.190476 \\times 4.5 = 27.857142\n\\]  \nPlus \\(6.190476 \\times 0.046 \\approx 0.284762\\)  \nTotal:  \n\\[\n27.857142 + 0.284762 \\approx 28.141904 \\text{ litres}\n\\]\n\n**Step 3: Calculate the cost in pounds.**  \nPetrol is £1.46 per litre.  \n\\[\n\\text{Cost} = 28.141904 \\times 1.46\n\\]  \nFirst:  \n\\[\n28.141904 \\times 1 = 28.141904\n\\]  \n\\[\n28.141904 \\times 0.46 = 28.141904 \\times 0.4 = 11.2567616\n\\]  \n\\[\n28.141904 \\times 0.06 = 1.68851424\n\\]  \nAdd:  \n\\[\n11.2567616 + 1.68851424 = 12.94527584\n\\]  \nNow add the whole part:  \n\\[\n28.141904 + 12.94527584 = 41.08717984\n\\]\n\n**Step 4: Round to the nearest 10p.**  \n£41.08717984 rounded to the nearest 10p means nearest £0.10.  \nThe number is between £41.00 and £41.10.  \nThe second decimal is 8 (in 41.08…), which is ≥ 5, so we round up:  \n\\[\n\\boxed{41.10}\n\\]  \n\nSo the fuel cost is **£41.10**.",
   "latency_ms": 9699,
   "cost": 0.0001456,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct calculation and rounding, clear steps, though slightly verbose with unnecessary intermediate approximations."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the fuel cost step-by-step, arriving at the correct answer of £41.10. It follows all instructions perfectly and is clear and easy to follow."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct: 260/42 gallons, converted using 4.546 litres per gallon, then multiplied by £1.46. £41.087... correctly rounds to £41.10 to the nearest 10p. Clear step-by-step presentation."
    }
   ]
  },
  {
   "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 the two days had different numbers of transactions, so the Tuesday average (with more transactions) carries more weight. The correct overall average is (50×20 + 150×40) ÷ (50 + 150) = (1000 + 6000) ÷ 200 = 7000 ÷ 200 = **£35**.",
   "latency_ms": 2749,
   "cost": 0.0000170128,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math and explanation, but not a single line as requested; minor instruction deviation."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 9,
     "violates": false,
     "reasoning": "The response accurately explains the weighted average concept and calculates the correct overall average of £35, all within a single line of text as requested."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly explains that unequal transaction counts require a weighted average and accurately calculates £35. It is presented as one line and is clear, concise, and useful."
    }
   ]
  },
  {
   "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": "## Estimate: 1,740 working hours per year\n\n### Assumptions\n\n1. **Weekly working hours**: 37.5 hours per week (a common full-time contract in the UK, e.g., for office workers).\n2. **Holiday entitlement**: 28 days of paid leave per year (the statutory minimum, including bank holidays), which equates to 5.6 weeks.\n3. **No other absences**: Sick leave, unpaid leave, or public holidays beyond the 28-day bundle are not considered (i.e., only contracted working days are counted).\n\n### Calculation\n- Working weeks per year: 52 weeks − 5.6 weeks = 46.4 weeks\n- Total hours: 46.4 × 37.5 = 1,740 hours\n\nAlternatively: 260 working days (52 weeks × 5 days) − 28 holidays = 232 days; 232 × 7.5 hours/day = 1,740 hours.\n\n### Sensitivity of Assumptions\nThe **weekly hours assumption** moves the answer most.  \n- A change from 37.5 to 40 hours (a 6.7% increase) raises the total by about 116 hours (to 1,856).  \n- A change in holiday entitlement from 28 to 33 days (a 17.9% increase in holidays) reduces the total by only about 37.5 hours (to 1,702.5).  \n\nThus, the weekly hours figure has a larger proportional impact on the estimate.",
   "latency_ms": 15680,
   "cost": 0.000472484,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Reasonable estimate with clear assumptions and correct math; sensitivity analysis slightly muddled but conclusion plausible. Clear, concise, useful for a professional."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions. It provides a clear estimate, lists exactly three assumptions, and accurately identifies and explains which assumption moves the answer the most. Highly useful and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate UK-based estimate with three clear assumptions, correct arithmetic, a useful cross-check, and a quantified sensitivity comparison. It directly identifies weekly contracted hours as the assumption with the largest effect under the s"
    }
   ]
  },
  {
   "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 ISA returns depend on variable market performance and choice of assets. Assuming 5% annual growth (a balanced fund average), £10,000 becomes ~£16,289. With 3% (cautious estimate), it’s ~£13,439; with 7% (bullish), ~£19,672. Real returns after inflation could be 1–2% lower.",
   "latency_ms": 5219,
   "cost": 0.0000180789,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, concise, meets word limit, gives clear range with stated assumptions; minor lack of explicit word count check but content is solid and useful."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Follows all instructions perfectly. The math is accurate, the explanation is clear and concise, and it fits well within the word limit."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Accurately explains uncertainty and gives correct 10-year compound-growth figures for stated 3%, 5%, and 7% assumptions. Clear and under 80 words. Minor weakness: assumptions do not explicitly state fees, contributions, or whether rates are"
    }
   ]
  }
 ]
}