{
 "entity": "glm-5-2",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "z-ai/glm-5.2",
 "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": 97,
 "caps": 0,
 "cost_usd": 0.1271,
 "started_at": "2026-08-14T12:48:58.692Z",
 "finished_at": "2026-08-14T12:50:49.434Z",
 "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": 1943,
   "cost": 0.0017,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calculation, avoids the common error, follows one-line format instructions, concise and clear."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, providing accurate calculations in exactly one line each without making the common mistake."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both calculations are correct: £240 inclusive of 20% VAT gives £200 ex-VAT and £40 VAT. It uses one clear line for each and 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. \nThe rise as a percentage of the original rate is 25%.",
   "latency_ms": 5903,
   "cost": 0.00171835048,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations (1 pp, 25%), both numbers present, concise, follows one-sentence-each format."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows all instructions, correctly calculating both the percentage point increase and the percentage increase, and presents them in exactly two sentences."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both requested measures are correct: the increase is 1 percentage point and 25% relative to the original 4% rate. It uses one sentence for each answer and includes both numbers clearly."
    }
   ]
  },
  {
   "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": "Here is the breakdown of the prices per 100ml:\n\n**Option 1: 750ml for £3.15**\n* Calculation: £3.15 ÷ 7.5 (since 750ml is 7.5 x 100ml)\n* Price per 100ml: **£0.42**\n\n**Option 2: 1.2L for £4.80**\n* Calculation: £4.80 ÷ 12 (since 1.2L = 1200ml, which is 12 x 100ml)\n* Price per 100ml: **£0.40**\n\n**Winner:** The **1.2L for £4.80** is cheaper per 100ml.",
   "latency_ms": 2880,
   "cost": 0.002441,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations (£0.42 vs £0.40), correct winner, clear format, concise, meets all task requirements."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly answers the prompt, providing accurate calculations for both options to the nearest penny and correctly identifying the cheaper option. It is clear, concise, and highly useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both unit-price calculations are correct to the nearest penny, and the cheaper option is correctly identified. The response directly follows the requested format and is clear."
    }
   ]
  },
  {
   "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": "Mortgage interest is charged on the amount you owe. Early in a 25-year mortgage, your debt is at its highest, so you are paying the most interest. Overpaying £100 a month at the start immediately shrinks your debt. This means you are charged less interest every single month for the next 20-plus years. In contrast, making those same overpayments in the final five years only saves interest on a much smaller balance for a short time, missing out on decades of savings.",
   "latency_ms": 105622,
   "cost": 0.0039752,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, no formulas, plain English explanation. Slightly over 90 words (~85 actually fine, let's count: appears ~86 words, within limit). Minor redundancy but concise overall."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly explains the concept in plain English without formulas. It accurately describes how early overpayments compound savings over time, and it strictly adheres to the under 90-word limit (82 words)."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Clear, accurate plain-English explanation. It correctly links earlier overpayments to reducing a larger balance and avoiding interest for much longer. It is under 90 words, uses no formulas, and directly contrasts late overpayments."
    }
   ]
  },
  {
   "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": "Remaining cost to split = £187.50 - £12.50 = £175.00\nEach of the four pays = £175.00 / 4 = £43.75",
   "latency_ms": 2073,
   "cost": 0.0016134,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, exactly two lines as requested, clear and concise."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the correct amount, clearly showing the working in exactly two lines as requested."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly excludes the £12.50 meal from the total and divides the remaining £175 equally among four, giving £43.75 each. It follows the requested two-line working format and is clear and concise."
    }
   ]
  },
  {
   "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": "Here are the calculations for a £5,000 investment at 4% annual interest over 3 years:\n\n**1. Simple Interest**\n* Formula: Principal + (Principal × Rate × Time)\n* Calculation: £5,000 + (£5,000 × 0.04 × 3) = £5,000 + £600\n* **Final Amount: £5,600.00**\n\n**2. Annual Compounding**\n* Formula: Principal × (1 + Rate)^Time\n* Calculation: £5,000 × (1.04)^3 = £5,000 × 1.124864\n* **Final Amount: £5,624.32**\n\n**3. The Difference**\n* £5,624.32 - £5,600.00\n* **Difference: £24.32**",
   "latency_ms": 14064,
   "cost": 0.0034242,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations correct to the penny, clearly formatted, matches task requirements exactly."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the simple interest, compound interest, and the difference, providing the exact amounts to the penny as requested. It is clear, concise, and highly useful."
    },
    {
     "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. It directly answers all requested parts with clear formulas and concise presentation."
    }
   ]
  },
  {
   "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 second 10% discount is applied to the already-reduced price of £60, not the original £80. Because the discounts compound sequentially on the new subtotal, the total reduction is 32.5% rather than a flat 35%.",
   "latency_ms": 14608,
   "cost": 0.0039152,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math (80*0.75*0.9=54), correct explanation, within two-sentence plus number constraint though number given first, minor formatting deviation but content accurate and clear."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly calculates the final price, accurately explains the sequential discounting in exactly two sentences, and includes the final number as requested."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly calculates £80 × 75% × 90% = £54 and accurately explains that the second discount applies after the first, producing a 32.5% total reduction. It uses a number plus two clear 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": "£29,900 ÷ 1.15 = £26,000",
   "latency_ms": 11980,
   "cost": 0.0015668,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, correct result (26000*1.15=29900), one-line format as requested, avoids the common wrong approach."
    },
    {
     "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": "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. It provides the requested one-line calculation and 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": "Here is the step-by-step calculation to find the cost of the journey:\n\n**Step 1: Calculate the number of gallons of fuel needed for the journey**\n*   Distance = 260 miles\n*   Fuel efficiency = 42 miles per gallon\n*   Gallons needed = 260 ÷ 42 = 6.190476... gallons\n\n**Step 2: Convert the gallons into litres**\n*   1 gallon = 4.546 litres\n*   Litres needed = 6.190476... × 4.546 = 28.1419... litres\n\n**Step 3: Calculate the total cost of the fuel**\n*   Cost per litre = £1.46\n*   Total cost = 28.1419... × £1.46 = £41.0871...\n\n**Step 4: Round the cost to the nearest 10p**\n*   The total cost is £41.087...\n*   Looking at the hundredths digit (8), we round the tenths digit up.\n*   Rounded cost = £41.10\n\nThe 260-mile journey costs **£41.10** in fuel.",
   "latency_ms": 16091,
   "cost": 0.0048798,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Calculations correct, clear step-by-step format, rounding accurate to £41.10, concise and useful for non-technical reader."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response accurately calculates the fuel cost step-by-step, arriving at the correct final answer of £41.10. It follows all instructions perfectly and is clear and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "All calculations are correct: fuel required, litre conversion, total cost, and rounding to the nearest 10p. It shows each requested step clearly and reaches £41.10."
    }
   ]
  },
  {
   "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 days have different numbers of transactions (it is a weighted average skewed toward Tuesday's higher sales), making the actual overall average £35.",
   "latency_ms": 12193,
   "cost": 0.0012212,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (£35), correctly explains weighted average, concise one-line answer as requested."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "The response perfectly follows the one-line constraint, correctly explains the concept of a weighted average due to different transaction volumes, and accurately calculates the overall average as £35."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly identifies that differing transaction counts require a weighted average and gives the correct overall average: (£20×50 + £40×150) ÷ 200 = £35. It is concise, clear, and in one 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:**\nRoughly **1,750 working hours** in a UK full-time year. \n\n**The 3 Assumptions:**\n1. **Standard weekly hours:** The baseline work week is 37.5 hours (a common UK standard, sitting between the 35-hour weeks often seen in the public sector and the 40-hour weeks common in the private sector). \n2. **Paid time off:** The worker takes 28 days of paid leave per year. This is the UK statutory minimum (5.6 weeks), which typically includes the 8 public (bank) holidays. This leaves roughly 46.5 working weeks in the year.\n3. **Sickness and absence:** The worker takes zero days off for sickness or other unpaid leave. \n\n*(The math: 37.5 hours × 46.5 weeks = 1,743.75 hours).*\n\n**Which assumption moves the answer most?**\nThe **standard weekly hours** assumption moves the answer the most. \n\nIf you change the weekly hours from 35 to 40 (a very common range in the UK), the annual total shifts by about **230 hours** (from ~1,625 to ~1,860 hours). \n\nBy contrast, if you change the time off assumption—for example, by adding a full week of sickness or an extra week of annual leave—the annual total only shifts by about **37.5 hours**. Therefore, the baseline length of the work week has a vastly larger impact on the final number than variations in holidays or sickness.",
   "latency_ms": 17730,
   "cost": 0.0051944,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, well-structured, correct math, clear assumptions and sensitivity analysis. Minor: only 46.5 vs 52 weeks check slightly informal, 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 well-reasoned assumptions, and accurately identifies and explains which assumption impacts the final number the most. Highly useful "
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Clear estimate, assumptions, and sensitivity comparison. The arithmetic is sound using rounded 46.5 weeks. Minor caveat: 28 days equals 5.6 weeks, leaving 46.4 weeks, and actual UK contractual hours and leave vary substantially."
    }
   ]
  },
  {
   "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 fluctuate based on unpredictable market conditions, interest rates, and whether you hold cash or stocks. \n\nAssuming no further contributions, a defensible range is **£13,400 to £17,900**:\n* **£13,400:** Assumes a Cash ISA averaging 3% annual interest.\n* **£17,900:** Assumes a Stocks & Shares ISA averaging 6% annual growth.",
   "latency_ms": 14017,
   "cost": 0.0029646,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, concise, meets word limit, states assumptions and range as requested; minor rounding but defensible."
    },
    {
     "judge": "google/gemini-3.1-pro-preview",
     "score": 10,
     "violates": false,
     "reasoning": "Flawless response. It strictly meets the word count constraint (54 words), accurately explains the uncertainty, provides a mathematically sound range, and clearly states the underlying growth assumptions. Highly useful and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Clear, accurate compound-growth estimates with stated 3% and 6% assumptions, and it explains uncertainty. Minor limitation: the range compares product types rather than acknowledging that investment returns can fall or that fees may reduce "
    }
   ]
  }
 ]
}