{
 "entity": "gpt-5-5",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "openai/gpt-5.5",
 "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": 98,
 "caps": 1,
 "cost_usd": 0.1769,
 "started_at": "2026-08-14T12:51:22.560Z",
 "finished_at": "2026-08-14T12:51:54.153Z",
 "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": 3654,
   "cost": 0.00272,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, avoids common error, one-line each as instructed, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response is perfectly accurate, follows all constraints, and clearly shows the correct calculations in one line each without making the common mistake."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc shown in one line each; avoids common error; clear, concise, fully 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 as a percentage is **25%**.",
   "latency_ms": 3203,
   "cost": 0.002925,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct values (1 pp, 25%), both numbers present, but instructions asked for one sentence each combining both explanations concisely; response is close but slightly terse/split into fragments rather than full sentences."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing accurate calculations in exactly two sentences with both numbers clearly stated."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct 1 pp and 25%; two single sentences; both numbers present; clear and useful."
    }
   ]
  },
  {
   "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 = **£0.42 per 100ml**\n- **1.2L for £4.80:** £4.80 ÷ 12 = **£0.40 per 100ml**\n\n**Winner: 1.2L for £4.80** — it’s cheaper at **40p per 100ml**.",
   "latency_ms": 3815,
   "cost": 0.005095,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Calculations correct: £3.15/750ml=42p, £4.80/1.2L=40p per 100ml. Winner correctly identified, clear and concise format."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the per-100ml price for both options, rounds to the nearest penny, correctly identifies the winner, and is extremely clear and concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc and comparison; fully follows task; clear and concise for non-technical user."
    }
   ]
  },
  {
   "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 cuts the outstanding mortgage balance when it’s still large. Because interest is charged on what you still owe, that smaller balance means you’re charged less interest every month for many years. Those savings then keep building over the remaining term. In the final 5 years, the balance is already much lower and there’s little time left for the reduced interest to add up, so the same £100/month has a much smaller effect.",
   "latency_ms": 3503,
   "cost": 0.0044,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Clear, accurate, no formulas, plain English, under 90 words (~78), fully addresses the task."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly explains the concept in plain English without formulas, accurately highlighting how early principal reduction compounds interest savings over time. It strictly adheres to the under 90-word constraint (75 words)."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate plain-English explanation of compound interest effect; under 90 words, no formulas, fully meets all constraints."
    }
   ]
  },
  {
   "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": 3641,
   "cost": 0.00395,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct arithmetic, concise two-line working as requested, clear and useful for a non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, provides correct math, and is formatted exactly in two lines as requested."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact two-line working; arithmetic correct; fully meets task; clear and concise for any user."
    }
   ]
  },
  {
   "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:** £5,600.00  \n- **Annual compounding:** £5,624.32  \n- **Difference:** £24.32  \n\nAnnual compounding gives **£24.32 more** than simple interest.",
   "latency_ms": 4092,
   "cost": 0.004245,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Both calculations correct to the penny, difference correct, clear and concise format."
    },
    {
     "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 them clearly and concisely to the penny as requested."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Calculations exact to the penny; all required figures and difference provided 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\n\nThe discounts are applied sequentially: £80 × 0.75 × 0.90 = £54.  \nIt is not 35% off because the 10% is taken from the already-discounted £60, making the total discount 32.5%, not 35%.",
   "latency_ms": 2992,
   "cost": 0.00457,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Correct math and explanation, but exceeds the two-sentence limit (three sentences plus the number)."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the final price, accurately explains the sequential discount math, and strictly adheres to the two-sentence plus number constraint."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and explanation; exactly two sentences plus 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": "£29,900 ÷ 1.15 = **£26,000**",
   "latency_ms": 3409,
   "cost": 0.00336,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation, avoids the common wrong method, concise one-line format as requested."
    },
    {
     "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 concise."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct one-line calc avoiding the common error; fully follows all task constraints; clear and useful."
    }
   ]
  },
  {
   "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. **Work out how many gallons are needed:**\n\n\\[\n\\frac{260 \\text{ miles}}{42 \\text{ miles per gallon}} = 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. **Work out the cost:**\n\n\\[\n28.1419 \\times £1.46 = £41.087\n\\]\n\n4. **Round to the nearest 10p:**\n\n\\[\n£41.087 \\approx £41.10\n\\]\n\n**The 260-mile journey costs about £41.10 in fuel.**",
   "latency_ms": 5431,
   "cost": 0.009815,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear steps, matches nearest 10p rounding accurately (~£41.09→£41.10). Concise and well formatted."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, accurately calculates the cost step-by-step, and correctly rounds to the nearest 10p. It is clear, concise, and highly useful."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate stepwise calc and rounding to nearest 10p; fully follows show-steps request; clear and useful."
    }
   ]
  },
  {
   "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 there were more Tuesday transactions, the weighted average is \\((£20×50 + £40×150) ÷ 200 = £35\\), not £30.",
   "latency_ms": 10000,
   "cost": 0.00305,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (1000+6000)/200=35, explanation accurate, concise one-line answer as requested."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing a clear, accurate, one-line explanation of the weighted average and the correct final amount."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted avg explanation and calc in one 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": "Rough estimate: **about 1,700 working hours per year** for a UK full-time employee.\n\nCalculation:\n\n\\[\n(52 \\text{ weeks} - 6.6 \\text{ weeks off}) \\times 37.5 \\text{ hours/week}\n= 45.4 \\times 37.5\n\\approx 1,700 \\text{ hours}\n\\]\n\nAssumptions:\n\n1. **Full-time week = 37.5 hours**  \n   Common UK office pattern: 7.5 hours/day × 5 days.\n\n2. **Holiday = 25 days annual leave + 8 bank holidays**  \n   That is **33 days**, or **6.6 working weeks** off.\n\n3. **No adjustment for sickness, overtime, training, or unpaid leave**  \n   This is scheduled working time, not necessarily actual hours worked.\n\nThe assumption that moves the answer most is **weekly hours**.  \nFor example, using **40 hours/week** instead of 37.5 adds about:\n\n\\[\n45.4 \\times 2.5 \\approx 114 \\text{ hours}\n\\]\n\nBy contrast, changing holiday by 5 days only moves the estimate by about **37.5 hours**.",
   "latency_ms": 10771,
   "cost": 0.01976,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Clear, correct math, reasonable assumptions, addresses which assumption dominates. Minor: comparison could be more rigorous but overall solid and useful."
    },
    {
     "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 accurately identifies which assumption has the largest impact on the final number, with clear math to pro"
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate estimate and calc; clear assumptions; correctly identifies key driver; fully follows task; polished and useful."
    }
   ]
  },
  {
   "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 future interest rates, investment performance, fees, inflation and tax-rule changes, none of which are knowable in advance.\n\nIf it’s a diversified stocks-and-shares ISA and you assume **3%–7% annual growth after fees**, £10,000 in 10 years would be about **£13,400–£19,700**. A cash ISA would likely have a narrower but usually lower range, depending on future rates.",
   "latency_ms": 5778,
   "cost": 0.007855,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, states assumptions, gives range, concise; under 80 words. Minor quibble: could clarify inflation not deducted, but overall solid."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions. It is under 80 words, clearly explains why an exact figure is impossible, and provides an accurate, defensible range based on stated assumptions."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate explanation and range with stated assumptions; under 80 words; clear and useful for non-experts."
    }
   ]
  }
 ]
}