{
 "entity": "kimi-k3",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "moonshotai/kimi-k3",
 "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": 98,
 "caps": 2,
 "cost_usd": 0.1908,
 "started_at": "2026-08-14T12:55:54.404Z",
 "finished_at": "2026-08-14T12:56:51.530Z",
 "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** (check: £200 × 20% = £40 ✓)\n\nThe £240 represents 120% of the net price, so you divide by 1.20 rather than subtracting 20% of the gross.",
   "latency_ms": 9424,
   "cost": 0.005256,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, correct method avoiding the trap, clear one-line format with brief explanation. Accurate and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the ex-VAT price and VAT amount, shows the calculations in one line each as requested, and avoids the common mistake."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly derives £200 net by dividing the VAT-inclusive price by 1.20, then calculates £40 VAT. Provides one calculation line for each requested value and explicitly 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 in percentage points is **1 percentage point** (from 4% to 5%).\n\nThe rise as a percentage is **25%**, since the increase of 1 relative to the original 4 equals 1/4 = 25%.",
   "latency_ms": 1476,
   "cost": 0.003609,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct, clear, meets one-sentence-each instruction closely, both numbers present, concise and accurate."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing accurate calculations in exactly one sentence each, and explicitly includes both required numbers."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly states a 1 percentage-point increase and a 25% relative increase. It provides one sentence for each requested answer, 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": "**750ml for £3.15:** £3.15 ÷ 7.5 = **42p per 100ml**\n\n**1.2L (1200ml) for £4.80:** £4.80 ÷ 12 = **40p per 100ml**\n\n**Winner: the 1.2L bottle** at 40p per 100ml — it's 2p cheaper per 100ml than the 750ml bottle.",
   "latency_ms": 10474,
   "cost": 0.005571,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculations, clear format, names winner as required, concise 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, clearly identifies the winner, and is perfectly concise and easy to read."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both unit-price calculations are correct: £3.15/7.5=42p and £4.80/12=40p per 100ml. It rounds appropriately, identifies the cheaper option, and clearly states the 2p difference."
    }
   ]
  },
  {
   "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": "Interest is charged on whatever you still owe. Early in a mortgage the balance is huge, so interest makes up most of each payment. An extra £100 then shrinks the balance, and that smaller balance keeps saving you interest every month for twenty-plus years — the savings snowball. Overpay near the end and the balance is already small and mostly principal; your £100 only reduces interest for a few remaining months, so there's barely any interest left to save.",
   "latency_ms": 21264,
   "cost": 0.012648,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate, clear, no formulas, plain English, under 90 words (approx 85), directly addresses the question well."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless explanation. It perfectly captures the compounding effect of early overpayments in plain English, strictly adheres to the word count, and uses zero formulas. Highly useful and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate, plain-English explanation of how early balance reduction avoids interest over many more months. It directly compares early versus final-five-year overpayments, stays under 90 words, and uses no formulas."
    }
   ]
  },
  {
   "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": "**Working:**\n\n£187.50 − £12.50 = £175.00 (the amount left for the four to split)\n\n£175.00 ÷ 4 = **£43.75 each**",
   "latency_ms": 5393,
   "cost": 0.003219,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, two-line working as requested, clear and concise for a non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The math is perfectly correct and easy to follow, but the response includes extra lines (a title and blank lines), violating the strict 'two lines' constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "The arithmetic is correct: removing £12.50 leaves £175.00, which divided among four is £43.75 each. It provides exactly two working lines and clearly identifies the requested amount."
    }
   ]
  },
  {
   "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: £5,000 + (£5,000 × 0.04 × 3) = **£5,600.00**\n\nAnnual compounding: £5,000 × 1.04³ = **£5,624.32**\n\nDifference: **£24.32** more with annual compounding.",
   "latency_ms": 8430,
   "cost": 0.004617,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate calculations, correct to the penny, clear and concise format matching the task exactly."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates both simple and compound interest to the penny, provides the correct difference, and is exceptionally clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct: simple interest is £5,600.00, annual compounding is £5,624.32, and the difference is £24.32. It provides each requested figure clearly and to the penny."
    }
   ]
  },
  {
   "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 25% discount reduces £80 to £60, and the 10% checkout discount then takes £6 off that, leaving £54. It's not 35% off because the second discount applies to the already-reduced price rather than the original — successive discounts multiply (0.75 × 0.90 = 0.675), giving a total reduction of 32.5%, not 35%.",
   "latency_ms": 7838,
   "cost": 0.003657,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Math correct (£54), explanation accurate, but exceeds two-sentence limit (three sentences plus bolded number) and formatting differs from requested constraint."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the final price, explains the math clearly, and strictly adheres to the constraint of two sentences maximum plus the number."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correct final price and explanation: discounts apply sequentially, yielding a 32.5% total reduction. It stays within two explanatory sentences and clearly provides the 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**\n\nThe new salary is 115% of the old one, so divide by 1.15 (not multiply by 0.85, which would wrongly give £25,415). Check: £26,000 × 1.15 = £29,900 ✓",
   "latency_ms": 1639,
   "cost": 0.003333,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, avoids the common error, clear one-line formula with verification, concise and accurate."
    },
    {
     "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 the 15% increase by dividing £29,900 by 1.15, giving £26,000. Includes the requested one-line calculation and a clear verification; it explicitly avoids the stated 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": "# Fuel Cost Calculation\n\n## Step 1: Work out gallons needed\n\n$$\\text{Gallons} = \\frac{260 \\text{ miles}}{42 \\text{ mpg}} = 6.19 \\text{ gallons (approx)}$$\n\n## Step 2: Convert gallons to litres\n\n$$6.1905 \\times 4.546 = 28.14 \\text{ litres (approx)}$$\n\n## Step 3: Work out the cost\n\n$$28.14 \\times £1.46 = £41.09 \\text{ (approx)}$$\n\n## Step 4: Round to the nearest 10p\n\n$$£41.09 \\rightarrow \\boxed{£41.10}$$\n\n**The 260-mile journey costs approximately £41.10 in fuel.**",
   "latency_ms": 17318,
   "cost": 0.011115,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear steps, accurate rounding to nearest 10p, well formatted and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the fuel cost, shows each step clearly, and correctly rounds to the nearest 10p. It is perfectly tailored for a non-technical professional."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are accurate: 260/42 gallons, converted using 4.546 litres per gallon, then multiplied by £1.46. £41.09 correctly rounds to £41.10 to the nearest 10p. Steps are clear and complete."
    }
   ]
  },
  {
   "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": "Because Tuesday's £40 average comes from three times as many transactions, it pulls the overall figure toward it — the weighted average is (£20×50 + £40×150) ÷ 200 = £7,000 ÷ 200 = **£35**, not the simple midpoint of £30.",
   "latency_ms": 2601,
   "cost": 0.0037422,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, clear explanation, though slightly longer than strictly one line but delivered as a single sentence."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing a clear, accurate explanation and the correct calculation 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 computes £35 accurately. It directly answers why £30 is wrong and gives the result clearly in one sentence."
    }
   ]
  },
  {
   "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: ~1,700 hours per year\n\n**Quick calculation:**\n- 52 weeks × 37.5 hrs = 1,950 hrs\n- Minus 5.6 weeks statutory leave (28 days incl. bank holidays) = −210 hrs\n- Minus ~5 days sickness absence = −38 hrs\n- **≈ 1,700 hrs** (sensible range: 1,650–1,800)\n\n**Assumptions it rests on:**\n1. **37.5-hour contracted week** — the UK full-time norm, though contracts range from ~35 to 40 hours.\n2. **28 days of leave** — the statutory minimum (20 days + 8 bank holidays); many employers give 25 days + bank holidays, i.e. 33 total.\n3. **Typical sickness absence (~4–6 days)** and no unpaid leave, sabbaticals, or major overtime in either direction.\n\n**Which assumption moves the answer most: the weekly hours.**\n\nBecause it's multiplied by ~46 working weeks, a 1-hour change in the contracted week shifts the annual total by ~46 hours. Moving from a 35-hour to a 40-hour contract swings the answer by ~230 hours. By contrast, 5 extra days of leave only removes ~38 hours, and even a generous-to-minimum leave swing is under 100 hours. The multiplicative assumption dominates; the additive ones are rounding errors by comparison.",
   "latency_ms": 10690,
   "cost": 0.0204942,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Reasonable, well-structured estimate with clear assumptions and correct identification of dominant driver; minor debatable precision but overall accurate and useful."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless response. It provides a clear estimate, explicitly lists three well-reasoned assumptions, and correctly identifies which assumption has the largest impact with a clear mathematical explanation."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Clear, numerically correct estimate with relevant assumptions and a sound sensitivity explanation. Minor issue: the stated 1,650–1,800 range does not fully reflect the mentioned 35–40-hour contract range, especially at 35 hours."
    }
   ]
  },
  {
   "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 — it depends on what the ISA holds (cash or investments), future interest rates, market returns, and fees, none of which are knowable now.\n\nWith stated assumptions on £10,000:\n- 2% growth (cautious/cash): ≈ £12,200\n- 5% growth (moderate investments): ≈ £16,300\n- 7% growth (strong markets): ≈ £19,700\n\nA defensible range: roughly £12,000–£20,000 before inflation, so real spending power will be lower.",
   "latency_ms": 26618,
   "cost": 0.016221,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, concise, meets word limit, gives defensible range with assumptions; minor nitpick on precise word count but well within 80 words."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, staying under the 80-word limit (68 words). It clearly explains why an exact figure is impossible, provides accurate calculations based on stated assumptions, and offers a highly useful, real"
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Accurately explains uncertainty and gives correct 10-year compounded values for stated 2%, 5%, and 7% assumptions. Clear, useful, and under 80 words. Minor omission: it does not explicitly say the rates are annual and compounded, though cal"
    }
   ]
  }
 ]
}