{
 "entity": "deepseek-v4-pro",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "deepseek/deepseek-v4-pro",
 "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": 96,
 "caps": 3,
 "cost_usd": 0.1063,
 "started_at": "2026-08-14T12:48:04.831Z",
 "finished_at": "2026-08-14T12:48:58.686Z",
 "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": 3834,
   "cost": 0.000786064,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, avoids common error, concise one-liners, meets task requirements accurately."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the ex-VAT price and VAT amount, avoids the common mistake, and strictly follows the one-line-each constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly removes 20% VAT by dividing the VAT-inclusive price by 1.20, yielding £200 ex-VAT, then calculates VAT as £40. Provides exactly one clear 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.  \nThe rise as a percentage is 25%.",
   "latency_ms": 5394,
   "cost": 0.000224373,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math (1pp, 25% increase), meets one-sentence-each requirement, both numbers present, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing two accurate, concise sentences that correctly calculate the percentage point increase and the percentage increase."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly states a 1 percentage point increase and a 25% relative increase. It uses one sentence for each requested measure, includes both numbers, and is clear and concise."
    }
   ]
  },
  {
   "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 price per 100ml for the 750ml bottle is £0.42 (42p), and for the 1.2L bottle it is £0.40 (40p). The 1.2L bottle is cheaper.",
   "latency_ms": 7753,
   "cost": 0.0004526175,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Calculations correct (42p vs 40p), winner correctly named, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the per-100ml prices, rounds to the nearest penny as requested, and correctly identifies the 1.2L bottle as the cheaper option. It is concise and directly answers the prompt."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both unit-price calculations are correct to the nearest penny: 42p per 100ml and 40p per 100ml. It clearly identifies the 1.2L bottle as cheaper."
    }
   ]
  },
  {
   "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": "Overpaying early shrinks the loan balance sooner, so you pay less interest on that smaller balance for the remaining decades. That monthly £100 keeps saving you interest year after year. In the final years, the balance is already low and the clock is almost up—each overpayment has far less time to prevent interest, so the total savings are tiny.",
   "latency_ms": 3593,
   "cost": 0.000703752,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, no formulas, clear plain English, under 90 words (fits well). Minor room for polish but solid answer."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly explains the concept in plain English without formulas, is well under the 90-word limit, and is highly useful and clear."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurately explains that early overpayments reduce the balance for much longer, cutting interest over remaining decades. It is plain English, concise, directly answers the comparison, uses no formulas, and is well under 90 words."
    }
   ]
  },
  {
   "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": "Let’s break it down:  \n\nTotal bill: £187.50  \nRemove the £12.50: £187.50 − £12.50 = £175.00 shared by 4 people.  \n\nEach of the four pays: £175.00 ÷ 4 = £43.75.",
   "latency_ms": 6372,
   "cost": 0.00016095,
   "task_score": 5,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Math correct, but task required exactly two lines of working; response has three lines/steps, violating format constraint."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The math is correct, but the response uses more than two lines to show the working, violating the formatting constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 5,
     "violates": true,
     "reasoning": "The calculation is correct: £187.50 minus £12.50 leaves £175, divided by four is £43.75 each. However, it does not follow the explicit requirement to show the 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": "Alright — let’s work through this step by step.\n\n---\n\n## **1. Simple Interest**\nThe formula for simple interest is:\n\n\\[\nA = P(1 + rt)\n\\]\n\nWhere:  \n- \\(P = 5000\\)  \n- \\(r = 0.04\\)  \n- \\(t = 3\\)\n\n\\[\nA = 5000 \\times (1 + 0.04 \\times 3)  \nA = 5000 \\times (1 + 0.12)  \nA = 5000 \\times 1.12  \nA = 5600.00\n\\]\n\nSo under **simple interest**, the final amount is **£5,600.00**.\n\n---\n\n## **2. Annual Compounding**\nThe formula for compound interest is:\n\n\\[\nA = P(1 + r)^t\n\\]\n\n\\[\nA = 5000 \\times (1.04)^3  \nA = 5000 \\times 1.124864  \nA = 5624.32\n\\]\n\nSo under **annual compounding**, the final amount is **£5,624.32**.\n\n---\n\n## **3. Difference**\n\\[\n5624.32 - 5600.00 = 24.32\n\\]\n\nThe difference is **£24.32**.\n\n---\n\n**Final answer:**\n- Simple interest: **£5,600.00**\n- Annual compounding: **£5,624.32**\n- Difference: **£24.32**",
   "latency_ms": 10439,
   "cost": 0.00073515,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Calculations correct, clear formatting, precise to penny, appropriate for non-technical user despite slightly technical presentation."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates both simple and compound interest to the penny, provides the correct difference, and presents the information clearly and concisely."
    },
    {
     "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 and is clear, though more detailed than necessary."
    }
   ]
  },
  {
   "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 £54.  \nIt is not 35% off because the second discount is applied to the already reduced price, not the original, so the total discount is 32.5%.",
   "latency_ms": 1219,
   "cost": 0.0001623,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (80*0.75*0.9=54), clear explanation of why not 35%, within two sentences plus number as required."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the final price and correctly explains the math in exactly two sentences, perfectly following all instructions and constraints."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly calculates £80 × 0.75 × 0.90 = £54 and accurately explains that successive discounts compound, producing a 32.5% total discount rather than 35%. It uses exactly two concise sentences."
    }
   ]
  },
  {
   "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": "Original salary = £29,900 ÷ 1.15 = £26,000.",
   "latency_ms": 7430,
   "cost": 0.000583074,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (26,000×1.15=29,900), one-line format as requested, avoids the common wrong method."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, provides the correct one-line calculation, avoids the common mistake, and is extremely clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly reverses a 15% increase by dividing £29,900 by 1.15, giving £26,000. It provides the requested one-line calculation and avoids the specified common error."
    }
   ]
  },
  {
   "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": "To find the fuel cost for a 260-mile journey:\n\n**Step 1: Calculate gallons needed**  \nMiles per gallon = 42  \nDistance = 260 miles  \nGallons = 260 ÷ 42 = 130/21 ≈ 6.190476 gallons\n\n**Step 2: Convert gallons to litres**  \n1 gallon = 4.546 litres  \nLitres = (130/21) × 4.546 = 590.98 ÷ 21 ≈ 28.141905 litres\n\n**Step 3: Calculate total cost**  \nPetrol price = £1.46 per litre  \nCost = 28.141905 × 1.46 ≈ £41.08718\n\n**Step 4: Round to the nearest 10p**  \n£41.08718 is between £41.00 and £41.10.  \nDistance to £41.10 = £0.01282, distance to £41.00 = £0.08718.  \n£41.10 is closer, so the cost rounded to the nearest 10p is **£41.10**.",
   "latency_ms": 31359,
   "cost": 0.00757736,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear steps, accurate rounding to £41.10, well-organized and appropriate for a non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, calculates the math accurately, shows each step clearly, and correctly rounds to the nearest 10p."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are accurate, each requested step is shown clearly, and £41.087... correctly rounds to £41.10 to the nearest 10p. It is concise and suitable for a non-technical reader."
    }
   ]
  },
  {
   "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 number of transactions differs between the two days, so the average must be weighted by transaction count; it is \\((50 \\times 20 + 150 \\times 40) / (50 + 150) = £35\\).",
   "latency_ms": 1388,
   "cost": 0.0001934,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (35), correct reasoning about weighting; concise one-line format matches instructions."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, accurately explains why the simple average is incorrect, provides the correct weighted average, and does so in exactly one line."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly explains that unequal transaction counts require a weighted average and calculates £35 accurately. It directly answers both parts in one concise 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": "**Estimate: about 1,700 working hours per year** for a typical UK full-time employee.\n\n**Assumptions:**\n\n1. **Weekly hours = 37.5 hours/week** — a common UK full-time contract.\n2. **Annual leave = 25 days + 8 bank holidays = 33 days** — i.e. 6.6 weeks off. This is typical, though the UK legal minimum is 28 days total.\n3. **No overtime, sickness, or other absence** — the person works all remaining working days.\n\n**Calculation:**\n\n\\[\n(52 - 6.6) \\times 37.5 = 45.4 \\times 37.5 = 1,702.5\n\\]\n\nSo roughly **1,700 hours/year**.\n\n**Which assumption moves the answer most?**  \nThe **weekly hours** assumption. For example, moving from 35 to 40 hours/week changes the estimate by about:\n\n\\[\n5 \\times 45.4 \\approx 227 \\text{ hours/year}\n\\]\n\nWhereas changing annual leave by 5 days only changes it by:\n\n\\[\n5 \\times 7.5 = 37.5 \\text{ hours/year}\n\\]\n\nSo the estimate is most sensitive to assumed weekly hours.",
   "latency_ms": 35211,
   "cost": 0.002808882,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate estimate, clear assumptions, correct math, correctly identifies weekly hours as most sensitive. Minor nitpick: sensitivity claim depends on range chosen, but reasoning is sound and clear."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly addresses all parts of the prompt. It provides a clear estimate, lists exactly three realistic assumptions, and correctly identifies and proves which assumption has the largest impact on the final number."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate calculation, exactly three clear assumptions, and a direct sensitivity comparison supports the conclusion that weekly contracted hours moves the estimate most. It is concise, practical, and appropriately caveated."
    }
   ]
  },
  {
   "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 investment returns, fees, inflation and market timing vary. Assuming a stocks and shares ISA grows at 2–7% a year after fees, £10,000 could become roughly £12,200–£19,700 in 10 years, before inflation. Lower growth reflects cautious holdings; higher growth assumes equity-like returns. Cash ISA returns would likely be lower.",
   "latency_ms": 10444,
   "cost": 0.000656676,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, concise, meets word limit, explains uncertainty and gives defensible range with stated assumptions; minor lack of inflation-adjusted note."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions. It explains why an exact figure is impossible, provides a mathematically accurate range based on clearly stated assumptions, and remains well under the 80-word limit."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurately explains why no exact value is possible, states clear 2–7% after-fee growth assumptions, gives mathematically sound 10-year values, notes inflation and cash ISA context, and stays well under 80 words."
    }
   ]
  }
 ]
}