{
 "entity": "gpt-5-6-terra",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "openai/gpt-5.6-terra",
 "judges": [
  "anthropic/claude-sonnet-5",
  "google/gemini-3.1-pro-preview",
  "x-ai/grok-4.5"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 99,
 "caps": 0,
 "cost_usd": 0.1197,
 "started_at": "2026-08-14T12:52:56.096Z",
 "finished_at": "2026-08-14T12:53:20.494Z",
 "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\nVAT amount: £240 − £200 = **£40**",
   "latency_ms": 1076,
   "cost": 0.000268,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, avoids the common error, concise one-line format as requested, clear for non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, correctly calculating the ex-VAT price and VAT amount in exactly one line each, while avoiding the common mathematical error."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct ex-VAT calc via /1.2; one-line each; avoids common error; clear and useful."
    }
   ]
  },
  {
   "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**.  \nThe rise is **25%**.",
   "latency_ms": 1015,
   "cost": 0.000177,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct math (1pp, 25%), but task asked for one sentence each explaining both concepts; response is terse two-line format lacking explanatory framing, slightly deviating from requested sentence style."
    },
    {
     "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 includes both numbers as requested. It is clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct 1 pp and 25% rises; two clear sentences; both numbers present; fully meets all criteria."
    }
   ]
  },
  {
   "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:** **42p per 100ml**\n- **1.2L for £4.80:** **40p per 100ml**\n\n**Winner:** The **1.2L for £4.80** option is cheaper, by **2p per 100ml**.",
   "latency_ms": 3257,
   "cost": 0.000737,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculations (42p vs 40p), clear winner named, concise format matches request exactly."
    },
    {
     "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": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct prices (42p, 40p), clear winner named; fully follows task with no errors or excess."
    }
   ]
  },
  {
   "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 cut the mortgage balance when it is highest, so every future monthly interest charge is calculated on a smaller amount. That saving then compounds over many years: less interest builds up, and more of each normal payment goes toward the loan itself. In the final five years, there is less balance left and far less time for reduced interest to accumulate, so the same £100 overpayment has a smaller overall effect.",
   "latency_ms": 2354,
   "cost": 0.00058,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, no formulas, plain English, concise; likely under 90 words. Minor: could be slightly clearer but solid."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless response. It perfectly explains the concept of compounding interest savings in plain English without formulas, and strictly adheres to the under 90-word constraint."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate plain-English reason, under 90 words, no formulas, clear and 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": "£187.50 − £12.50 = £175.00  \n£175.00 ÷ 4 = **£43.75 each**",
   "latency_ms": 1465,
   "cost": 0.00046,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, matches requested two-line format, clear and concise for a non-technical user."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the correct amount and strictly follows the constraint to show the working in exactly two lines. It is perfectly clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc in precisely two lines as required; clear and 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:** £5,000 × (1 + 0.04 × 3) = **£5,600.00**\n- **Annual compounding:** £5,000 × 1.04³ = **£5,624.32**\n- **Difference:** **£24.32**",
   "latency_ms": 2670,
   "cost": 0.000819,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Calculations correct to the penny, format clear and concise, meets all task requirements."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the simple interest, compound interest, and the difference, presenting the results clearly and concisely to the penny as requested."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calculations to the penny; fully addresses all parts clearly and concisely."
    }
   ]
  },
  {
   "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": "£54.00. The discounts apply sequentially: £80 × 0.75 × 0.90 = £54, which is an effective 32.5% discount, not 35% because the extra 10% is taken off the already discounted price.",
   "latency_ms": 1828,
   "cost": 0.00041,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation and explanation, concise, meets two-sentence-plus-number format reasonably well."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the final price, accurately explains the sequential discounting math, and strictly adheres to the length constraint."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and explanation; exactly two sentences plus price; 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": "£29,900 ÷ 1.15 = **£26,000**",
   "latency_ms": 1028,
   "cost": 0.00018,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation (26000×1.15=29900), one-line format, avoids the common wrong method as instructed."
    },
    {
     "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 as requested."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc shown in one line; avoids common error; fully meets all task needs clearly."
    }
   ]
  },
  {
   "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": "1. **Gallons needed for 260 miles:**\n\n\\[\n\\frac{260}{42}=6.1905\\text{ gallons}\n\\]\n\n2. **Convert gallons to litres:**\n\n\\[\n6.1905 \\times 4.546 = 28.1419\\text{ litres}\n\\]\n\n3. **Calculate fuel cost:**\n\n\\[\n28.1419 \\times £1.46 = £41.0872\n\\]\n\n4. **Round to the nearest 10p:**\n\n\\[\n£41.0872 \\approx £41.10\n\\]\n\n**The 260-mile journey costs approximately £41.10 in fuel.**",
   "latency_ms": 4800,
   "cost": 0.001879,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Math checks out, steps clearly shown, correct rounding to nearest 10p, concise and accurate."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, accurately calculating the cost step-by-step and correctly rounding to the nearest 10p. The layout is clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate stepwise calc and rounding; minor intermediate rounding but final correct. 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": "It’s a weighted average because Tuesday had more transactions: \\((50×£20 + 150×£40)÷200 = £35\\), not £30.",
   "latency_ms": 1265,
   "cost": 0.00028,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation and reasoning, matches one-line constraint, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows the one-line constraint, accurately calculates the overall average as £35, and clearly explains the concept of a weighted average."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted avg calc and explanation in one line; fully meets task, clear 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": "A reasonable estimate is **about 1,700–1,750 working hours per year** for a UK full-time employee.\n\nExample estimate: **1,740 hours/year**\n\nAssumptions:\n\n1. **37.5 hours per week** (e.g. 9–5 with a 30-minute unpaid lunch)  \n   - 37.5 × 52 = **1,950 hours**\n\n2. **28 days’ paid annual leave**, including bank holidays — the UK statutory minimum for a five-day worker  \n   - 28 days × 7.5 hours = **210 hours**\n\n3. No allowance for sickness absence, unpaid leave, or other non-working time  \n   - 1,950 − 210 = **1,740 hours**\n\nThe assumption that moves the answer most is usually **contracted weekly hours**. For example, a 35-hour week rather than 37.5 hours cuts the annual total by roughly **115 hours** after leave; a 40-hour week raises it by roughly the same amount. Holiday entitlement matters too, but an extra five days’ leave changes the total by only about **37.5 hours** for a 37.5-hour worker.",
   "latency_ms": 6531,
   "cost": 0.002656,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, shows assumptions and calculations, identifies dominant factor. Minor stylistic issue: gives 2-3 assumptions but structure slightly informal; overall strong and useful."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly answers the prompt, providing a clear estimate, exactly three well-explained assumptions, and correctly identifying which assumption impacts the final number the most. It is highly accurate, concise, and useful."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate UK estimate with clear assumptions and sensitivity analysis; fully meets all task requirements; concise and professional."
    }
   ]
  },
  {
   "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 is invested in, market returns, interest rates, fees, and any withdrawals or extra contributions.\n\nAssuming no changes and annual compounding, £10,000 could become roughly:\n\n- **£12,190** at **2%** a year  \n- **£19,670** at **7%** a year  \n\nA cash ISA may be nearer the lower end; a stocks-and-shares ISA could be higher or lower, including temporary losses.",
   "latency_ms": 4504,
   "cost": 0.001265,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, gives range with assumptions, concise, likely under 80 words; minor lack of explicit compounding formula detail but solid overall."
    },
    {
     "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 with clear assumptions, and stays well under the 80-word limit (66 words). Highly useful and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless: accurate calc, under 80 words, explains uncertainty then states assumptions and range clearly."
    }
   ]
  }
 ]
}