{
 "entity": "gemini-3-1-flash-lite",
 "entity_type": "model",
 "category": "Maths",
 "suite": "suite-2026-08-tasks2/maths",
 "model": "google/gemini-3.1-flash-lite",
 "judges": [
  "anthropic/claude-sonnet-5",
  "openai/gpt-5.6-terra",
  "x-ai/grok-4.5"
 ],
 "judge_protocol": "judge-2026-08",
 "anchors": "solo-2026-08-a",
 "score": 96,
 "caps": 1,
 "cost_usd": 0.078,
 "started_at": "2026-08-14T12:53:20.499Z",
 "finished_at": "2026-08-14T12:53:41.059Z",
 "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": "To find the ex-VAT price, you must divide the total by 1.2 (representing 100% + 20%):\n\n**Ex-VAT price:** £240 / 1.2 = £200\n**VAT amount:** £240 - £200 = £40",
   "latency_ms": 933,
   "cost": 0.0001195,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, avoids the common wrong answer, clear one-line format, concise and useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly divides the VAT-inclusive price by 1.2 to obtain £200 ex-VAT, then subtracts to find £40 VAT. It provides one clear calculation line for each requested amount."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math and method; calcs each on one line as required; clear and useful with brief intro."
    }
   ]
  },
  {
   "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 interest rate rose by 1 percentage point.\n\nThe interest rate increased by 25 percent.",
   "latency_ms": 421,
   "cost": 0.0000415,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Correct figures (1pp, 25%), meets task in two sentences, clear and concise, minor lack of explicit labeling but accurate and useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Both required measures are correct: 1 percentage point and 25 percent. The response uses one clear sentence for each and includes both numbers."
    },
    {
     "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 task requirements."
    }
   ]
  },
  {
   "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": "To find the cheaper option, we calculate the price per 100ml for each:\n\n**1. The 750ml bottle for £3.15:**\n*   First, find the price per ml: £3.15 ÷ 750 = £0.0042\n*   Multiply by 100 to get the price per 100ml: £0.0042 × 100 = **£0.42**\n\n**2. The 1.2L (1200ml) bottle for £4.80:**\n*   First, find the price per ml: £4.80 ÷ 1200 = £0.004\n*   Multiply by 100 to get the price per 100ml: £0.004 × 100 = **£0.40**\n\n**Conclusion:**\n*   750ml option: **£0.42 per 100ml**\n*   1.2L option: **£0.40 per 100ml**\n\nThe **1.2L bottle** is the winner (cheaper).",
   "latency_ms": 1130,
   "cost": 0.0004085,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear per-100ml prices rounded to nearest penny, correct winner identified, well structured and concise."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Calculations are correct: £3.15/750×100 = £0.42 and £4.80/1200×100 = £0.40. Both are shown to the nearest penny, and the cheaper 1.2L option is correctly identified."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct prices (£0.42, £0.40) and winner; fully follows task; clear and useful."
    }
   ]
  },
  {
   "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 calculated on your remaining balance. By overpaying early, you reduce the principal immediately, meaning less debt exists for the bank to charge interest on every subsequent month. Over 25 years, these smaller interest charges compound, saving you significant money. \n\nIf you wait until the final five years, the principal is already low, so there is less debt to \"shrink.\" You lose the benefit of years of compounding interest savings, making those late payments far less effective at reducing the total cost of your loan.",
   "latency_ms": 1360,
   "cost": 0.00016875,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Clear, accurate, no formulas, plain English. Slightly over ideal length but likely under 90 words; concise and useful."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 9,
     "violates": false,
     "reasoning": "Accurately explains that early overpayments reduce the balance for many more monthly interest calculations, whereas late payments have less time and a lower balance to affect. Plain English and under 90 words; “compound” is slightly impreci"
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate plain-English explanation of early principal reduction and compounding; 86 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": "Remaining cost to be split: £187.50 - £12.50 = £175.00\nEach of the four pays: £175.00 ÷ 4 = £43.75",
   "latency_ms": 810,
   "cost": 0.00009225,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct math, exactly two lines as required, clear and concise, useful for a non-technical reader."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly removes the £12.50 meal from the total and divides the £175.00 remainder equally among four. It gives exactly two clear working lines and directly answers the question."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct calc in precisely two lines as required; clear, useful, no flaws."
    }
   ]
  },
  {
   "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": "To calculate the final amounts for an initial principal ($P$) of £5,000 at an annual interest rate ($r$) of 4% (0.04) over a period ($t$) of 3 years, we use the following calculations:\n\n### 1. Simple Interest\nThe formula for simple interest is: $A = P(1 + rt)$\n\n*   **Interest:** £5,000 × 0.04 × 3 = £600\n*   **Final Amount:** £5,000 + £600 = **£5,600.00**\n\n---\n\n### 2. Annual Compounding\nThe formula for compound interest is: $A = P(1 + r)^t$\n\n*   **Year 1:** £5,000 × 1.04 = £5,200.00\n*   **Year 2:** £5,200 × 1.04 = £5,408.00\n*   **Year 3:** £5,408 × 1.04 = £5,624.32\n*   **Final Amount:** **£5,624.32**\n\n---\n\n### 3. The Difference\nTo find the difference between the two methods:\n\n*   £5,624.32 - £5,600.00 = **£24.32**\n\n***\n\n### Summary Table\n| Method | Final Amount |\n| :--- | :--- |\n| **Simple Interest** | £5,600.00 |\n| **Annual Compounding** | £5,624.32 |\n| **Difference** | **£24.32** |",
   "latency_ms": 1551,
   "cost": 0.000598,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculations, clear formatting, precise to the penny, matches task exactly with useful summary table."
    },
    {
     "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, and difference £24.32. It directly answers every requested item with clear workings and a concise summary."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Exact correct amounts to the penny; clear stepwise calc and summary; fully addresses task."
    }
   ]
  },
  {
   "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": "The final price is £54. It is not 35% off because the second discount is applied to the already reduced price rather than the original amount, meaning the 10% reduction is calculated on £60 instead of £80.",
   "latency_ms": 1005,
   "cost": 0.00009,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (£54), clear explanation of why not 35% off, follows two-sentence format with number."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correct final price and explanation: 25% off gives £60, then 10% off £60 gives £54, for a combined 32.5% discount rather than 35%. It uses two clear sentences."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc (£54), exact two sentences + number, clear explanation of sequential discounts."
    }
   ]
  },
  {
   "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": "To find the original salary, you divide the new salary by 1.15 (representing 115%):\n\n**£29,900 ÷ 1.15 = £26,000**",
   "latency_ms": 809,
   "cost": 0.00008775,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation, correct answer (26,000), avoids the wrong 15%-off method, concise one-line calculation shown clearly."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly reverses the 15% rise by dividing £29,900 by 1.15, giving £26,000. It includes a clear one-line calculation and avoids the specified common error."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct calc and result; shows required one-line division; avoids common error; clear, concise, 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": "To calculate the cost of the 260-mile journey, follow these steps:\n\n### Step 1: Calculate how many gallons of fuel are needed\nDivide the total distance by the car's fuel efficiency (miles per gallon).\n*   260 miles ÷ 42 miles/gallon = **6.190476... gallons**\n\n### Step 2: Convert the gallons into litres\nMultiply the number of gallons by the conversion factor (4.546 litres per gallon).\n*   6.190476... gallons × 4.546 litres/gallon = **28.14230... litres**\n\n### Step 3: Calculate the total cost\nMultiply the number of litres by the price per litre (£1.46).\n*   28.14230... litres × £1.46/litre = **£41.0877...**\n\n### Step 4: Round to the nearest 10p\nRounding £41.0877 to the nearest 10p:\n*   The value is £41.10.\n\n**Final Answer:**\nThe journey costs **£41.10**.",
   "latency_ms": 1530,
   "cost": 0.00041175,
   "task_score": 9,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate calculations, clear steps, correct rounding to £41.10, follows instructions well."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Correct method and final rounded cost (£41.10), with all requested steps shown. However, the litres figure is slightly inaccurate: 6.190476… × 4.546 = 28.141904… litres, not 28.14230…. This does not affect the final rounding."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Accurate stepwise calc and rounding; 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": "The overall average is not £30 because the higher volume of Tuesday transactions gives them more weight, resulting in a weighted average of £35.",
   "latency_ms": 674,
   "cost": 0.000057,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 9,
     "violates": false,
     "reasoning": "Correct calculation (£35), correctly explains weighting, concise one-line answer as requested."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Correctly explains that transaction counts require weighting and gives the accurate overall average: £35. It is concise, clear, and fits the requested one-line format."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Correct weighted avg £35; explains unequal volumes; single line as required; 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": "To estimate the number of working hours in a standard UK full-time year, we must account for the standard working week, statutory leave, and public holidays.\n\n### The Estimate\nA standard UK full-time year consists of approximately **1,650 to 1,750 working hours.**\n\n***\n\n### The Calculation (Assumptions)\nTo arrive at this figure, we use the following three assumptions:\n\n1.  **Standard Working Week:** We assume a standard contract of **37.5 hours per week** (the most common full-time benchmark in the UK).\n2.  **Statutory Leave:** We assume the legal minimum of **5.6 weeks of paid holiday** per year (which includes the 8 standard UK bank holidays).\n3.  **Total Weeks:** We assume a standard calendar year of **52 weeks**.\n\n**The Math:**\n*   Total weeks in a year: 52\n*   Minus statutory leave: 52 - 5.6 = 46.4 working weeks\n*   46.4 weeks × 37.5 hours = **1,740 hours per year.**\n\n*(Note: If an employee works a 35-hour week, this drops to 1,624 hours; if they work a 40-hour week, it rises to 1,856 hours.)*\n\n***\n\n### Which assumption moves the answer most?\n**Assumption #1 (The length of the working week)** is the most significant variable.\n\nWhile the amount of annual leave is relatively standardized by law (5.6 weeks), the \"standard\" working week in the UK varies significantly by industry and contract. \n\n*   **Impact of Assumption #1:** A shift from a 35-hour week to a 40-hour week creates a difference of **232 hours per year** (roughly 6 weeks of work).\n*   **Impact of Assumption #2:** Even if an employer offers \"generous\" leave (e.g., 30 days plus bank holidays, totaling roughly 8 weeks), the difference is only about 90–100 hours compared to the statutory minimum. \n\nBecause the weekly hour count acts as a multiplier applied to the entire year, small changes in the daily contract length have a much larger compounding effect on the annual total than variations in holiday allowance.",
   "latency_ms": 2581,
   "cost": 0.0007705,
   "task_score": 8,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 8,
     "violates": false,
     "reasoning": "Accurate, clear, well-structured with assumptions and correct identification of most impactful variable. Slightly verbose but appropriate for clarity; minor redundancy in final estimate range vs single value."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 8,
     "violates": false,
     "reasoning": "Clear calculation and all requested elements are present. Main estimate is sound under stated assumptions. Minor issue: 30 days plus 8 bank holidays is 7.6 weeks, implying about 75 extra hours at 37.5 hours/week, not 90–100."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 9,
     "violates": false,
     "reasoning": "Accurate estimate and math; clearly lists 3 assumptions and identifies the key driver with good impact comparison. Minor range vs point estimate only."
    }
   ]
  },
  {
   "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 provide an exact figure because investment returns are unpredictable and depend on market performance.\n\nAssuming a £10,000 initial investment with no further contributions:\n\n*   **Conservative (3% annual growth):** Approximately **£13,439**.\n*   **Moderate (6% annual growth):** Approximately **£17,908**.\n*   **Optimistic (9% annual growth):** Approximately **£23,674**.\n\nThese figures assume annual compounding and ignore inflation, which reduces your \"real\" purchasing power over time. Actual results will fluctuate based on your specific asset allocation and market conditions.",
   "latency_ms": 880,
   "cost": 0.00021875,
   "task_score": 10,
   "judges": [
    {
     "judge": "anthropic/claude-sonnet-5",
     "score": 5,
     "violates": true,
     "reasoning": "Content is accurate and useful, but exceeds 80-word limit (~90 words), violating explicit constraint."
    },
    {
     "judge": "openai/gpt-5.6-terra",
     "score": 10,
     "violates": false,
     "reasoning": "Accurately explains why no exact value is possible, gives correct 10-year compounded estimates with explicit assumptions, notes inflation and variability, and stays well under 80 words."
    },
    {
     "judge": "x-ai/grok-4.5",
     "score": 10,
     "violates": false,
     "reasoning": "Word count 69 <80; accurate FV calcs; clear why/no-exact + ranged assumptions; fully meets all criteria."
    }
   ]
  }
 ]
}