{
 "entity": "claude-fable-5",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "anthropic/claude-fable-5",
 "judges": [
  "google/gemini-3.1-pro-preview",
  "openai/gpt-5.6-terra",
  "x-ai/grok-4.5"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 96,
 "caps": 4,
 "cost_usd": 0.2595,
 "started_at": "2026-08-14T12:45:11.275Z",
 "finished_at": "2026-08-14T12:45:50.938Z",
 "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\n**VAT amount:** £240 − £200 = **£40**\n\nThe key point: the 20% was added to the ex-VAT price, so you must divide by 1.20 to reverse it. Subtracting 20% of £240 (£48) would wrongly give £192, because £48 is 20% of the *gross* price, not of the original net price. Check: £200 × 1.20 = £240 ✓",
   "latency_ms": 5293,
   "cost": 0.00986,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the ex-VAT price and VAT amount, showing each calculation on a single line as requested. It correctly avoids the common pitfall and provides a clear, concise explanation."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly divides the VAT-inclusive price by 1.20 to obtain £200, then calculates £40 VAT. Provides one calculation line for each requested amount, explicitly avoids the stated common error, and is clear and useful."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and answers; one-line calcs each; avoids common error; clear, useful extra check."
    }
   ]
  },
  {
   "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** (5% − 4% = 1), and as a percentage it is a **25% increase**, since the 1-point rise is one quarter of the original 4% rate (1 ÷ 4 = 0.25).",
   "latency_ms": 5042,
   "cost": 0.00611,
   "task_score": 5,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 5,
     "violates": true,
     "reasoning": "The response provides the correct numbers (1 percentage point and 25%) but combines them into a single sentence, violating the constraint to provide 'one sentence each'."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 5,
     "violates": true,
     "reasoning": "Both calculations are correct and both numbers appear, but the response gives them in one combined sentence rather than one sentence each, so it breaks the required format."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 5,
     "violates": true,
     "reasoning": "Correct 1 pp and 25%; both numbers present. But one combined sentence, not one each as required."
    }
   ]
  },
  {
   "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": "**Option 1: 750 ml for £3.15**\n- £3.15 ÷ 7.5 = **£0.42 per 100 ml**\n\n**Option 2: 1.2 L (1200 ml) for £4.80**\n- £4.80 ÷ 12 = **£0.40 per 100 ml**\n\n**Winner: the 1.2 L bottle** — it's 2p cheaper per 100 ml.",
   "latency_ms": 5722,
   "cost": 0.0104,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly 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 appropriately to the nearest penny, and the stated winner and 2p difference are correct. The response directly follows the requested format and is clear."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct prices (£0.42 and £0.40), right winner, clear format meeting all task needs."
    }
   ]
  },
  {
   "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, every month, for as long as you owe it. Overpay £100 early, and that £100 stops attracting interest for the next 25 years — and because your balance is lower, each subsequent payment clears more debt, compounding the benefit. The same £100 paid in the final five years only avoids a few years' interest, and on a small remaining balance where most of each payment is already going to capital anyway. Time is what does the heavy lifting.",
   "latency_ms": 6751,
   "cost": 0.01109,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless explanation. It perfectly captures the compounding effect of time on mortgage interest in plain English, uses no formulas, and strictly adheres to the under-90-word limit."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Clear, accurate plain-English explanation under 90 words. It correctly emphasizes reducing principal earlier and avoiding interest for longer. Minor imprecision: an early £100 overpayment does not always avoid interest for exactly 25 years,"
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate plain-English reason; 85 words; no formulas; clear, concise, fully 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": "**Working:**\n1. £187.50 − £12.50 = £175.00 remaining for the four to share\n2. £175.00 ÷ 4 = **£43.75 each**",
   "latency_ms": 3942,
   "cost": 0.00516,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The math is perfectly accurate, and the working is clearly shown in exactly two numbered lines as requested. It is highly useful, concise, and easy to understand."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Arithmetic is correct: subtracting £12.50 leaves £175.00, divided equally among four is £43.75 each. It provides the requested working in two numbered lines and is clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and exact two-line working as required; clear, concise, fully 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": "## Simple Interest\n- Interest = £5,000 × 0.04 × 3 = £600.00\n- **Final amount = £5,600.00**\n\n## Compound Interest (annual)\n- Final amount = £5,000 × (1.04)³ = £5,000 × 1.124864\n- **Final amount = £5,624.32**\n\n## Difference\n£5,624.32 − £5,600.00 = **£24.32**\n\nCompounding earns an extra £24.32 because interest in years 2 and 3 is also earned on previously accrued interest.",
   "latency_ms": 5250,
   "cost": 0.01304,
   "task_score": 10,
   "judges": [
    {
     "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 highly clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct to the penny: simple interest £5,600.00, annual compounding £5,624.32, difference £24.32. The response clearly distinguishes methods and briefly explains the source of the difference."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calculations to the penny for both methods and difference; clear, complete, and fully matches the request."
    }
   ]
  },
  {
   "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": "**Final price: £54.**\n\nThe discounts apply sequentially: 25% off £80 gives £60, then 10% off £60 gives £54. It's not 35% off because the second discount is taken from the already-reduced price, not the original — making the combined effect only 32.5% off.",
   "latency_ms": 4907,
   "cost": 0.0063,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Accurately calculates the final price and clearly explains the sequential discount logic. Adheres perfectly to the constraint of two sentences plus the number."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 5,
     "violates": true,
     "reasoning": "Correct calculation and clear explanation: £80 × 0.75 × 0.90 = £54, a 32.5% reduction. However, it has three sentences when counting “Final price: £54.”, exceeding the two-sentence maximum."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and explanation; exactly two sentences plus the number; clear and useful."
    }
   ]
  },
  {
   "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": "## Correct calculation\n\n**£29,900 ÷ 1.15 = £26,000**\n\n## Why this works\n\nThe new salary is 115% of the original (100% + 15% rise). So:\n\n$$\\text{original} \\times 1.15 = £29{,}900 \\quad\\Rightarrow\\quad \\text{original} = \\frac{£29{,}900}{1.15} = £26{,}000$$\n\n**Check:** £26,000 × 1.15 = £29,900 ✓\n\n## Why the common wrong answer fails\n\nTaking 15% off £29,900 gives £29,900 × 0.85 = **£25,415** — but this is wrong because the 15% would be calculated on the *new* (larger) salary, not the original one. Checking it confirms the error: £25,415 × 1.15 = £29,227.25 ≠ £29,900. ✗",
   "latency_ms": 6641,
   "cost": 0.01522,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the original salary, provides the requested one-line calculation, and correctly avoids the common pitfall while explaining why it's wrong. Highly clear and accurate."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "The calculation is correct: £29,900 ÷ 1.15 = £26,000. It explicitly avoids the stated common error, includes the requested one-line calculation, and gives clear verification and explanation."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct one-line calc and result; extras helpful but exceed the requested one-line focus slightly."
    }
   ]
  },
  {
   "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: Find how many gallons are needed**\n\n$$\\text{Gallons} = \\frac{260 \\text{ miles}}{42 \\text{ mpg}} = 6.1905 \\text{ gallons}$$\n\n**Step 2: Convert gallons to litres**\n\n$$\\text{Litres} = 6.1905 \\times 4.546 = 28.142 \\text{ litres}$$\n\n**Step 3: Calculate the cost**\n\n$$\\text{Cost} = 28.142 \\times £1.46 = £41.087$$\n\n**Step 4: Round to the nearest 10p**\n\n$$£41.087 \\approx \\boxed{£41.10}$$",
   "latency_ms": 7081,
   "cost": 0.02416,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, showing each step clearly and arriving at the correct final answer rounded to the nearest 10p."
    },
    {
     "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. The final £41.087 is correctly rounded to £41.10, with each requested step shown."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate calc and steps; minor intermediate rounding but correct final £41.10. Clear, useful, follows all."
    }
   ]
  },
  {
   "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 the days have unequal transaction counts, you must weight by volume — the overall average is (50×£20 + 150×£40) ÷ 200 = £7,000 ÷ 200 = **£35**, pulled toward Tuesday's £40 since it had three times as many sales.",
   "latency_ms": 5249,
   "cost": 0.0071,
   "task_score": 10,
   "judges": [
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing a clear, accurate, and concise explanation in exactly one line. The math is correct and easy to understand."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly explains that unequal transaction counts require a weighted average and computes £7,000 ÷ 200 = £35. It directly answers in one clear line."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted avg £35 in one clear line; fully meets task."
    }
   ]
  },
  {
   "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: roughly **1,700–1,750 hours per year**\n\n### The calculation\n\n**Assumption 1: Working week ≈ 37.5 hours**\nTypical UK full-time contracts range from 35 to 40 hours; 37.5 (9–5 with an unpaid lunch hour, or 9–5:30) is a common middle ground.\n\n**Assumption 2: Annual leave ≈ 5.6 weeks (28 days)**\nThis is the UK statutory minimum for full-timers, usually taken as ~20 days holiday + 8 bank holidays. Many employers offer a few days more.\n\n**Assumption 3: Negligible other absence**\nIgnoring sick leave, training days, etc. (or treating a few sick days as roughly offsetting).\n\n**The maths:**\n- 52 weeks − 5.6 weeks leave ≈ **46.4 working weeks**\n- 46.4 × 37.5 hours ≈ **1,740 hours**\n\n### Which assumption matters most?\n\n**The weekly hours figure.** Moving from 35 to 40 hours/week shifts the answer from ~1,625 to ~1,855 — a swing of over 230 hours (±7%). By contrast, adding or removing a week of holiday only moves the total by ~37 hours (±2%), and typical sick leave (4–5 days/year) is smaller still.\n\nSo if you need a single round number: **~1,750 hours**, but check the contracted weekly hours first if precision matters.",
   "latency_ms": 10381,
   "cost": 0.02982,
   "task_score": 10,
   "judges": [
    {
     "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, explicitly states three assumptions, and accurately identifies and explains which assumption impacts the final number the most. Highly useful and concis"
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Clear, accurate estimate with exactly three stated assumptions and correct arithmetic. It identifies the most influential assumption well. Minor issue: “9–5 with an unpaid lunch hour” is typically 35, not 37.5, hours per week."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate UK estimate with clear assumptions and sensitivity; fully addresses task; highly useful and concise."
    }
   ]
  },
  {
   "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 one can say exactly — returns depend on unknowable future market performance, your fund choices, fees, and interest rates. But here's a defensible range: at 2% annual growth (cautious/cash ISA), £10,000 becomes ~£12,200; at 5% (balanced stocks & shares ISA), ~£16,300; at 7% (equity-heavy, historical average), ~£19,700. All figures assume reinvested returns, no withdrawals, and are before inflation, which would reduce real spending power.",
   "latency_ms": 9302,
   "cost": 0.01044,
   "task_score": 10,
   "judges": [
    {
     "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 (66 words), clearly explains why an exact figure is impossible, and provides highly accurate, mathematically sound estimates with clear assumptions."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Clearly explains uncertainty, provides accurate 10-year compounded values across stated 2%, 5%, and 7% annual-growth assumptions, and notes reinvestment, no withdrawals, and inflation. It is concise, practical, and under 80 words."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate explanation and compound growth calcs; meets word limit and all task elements; clear and useful for non-experts."
    }
   ]
  }
 ]
}