claude-opus-5 × math

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Prompt

math1.2K tok cap

A SaaS product has 1,000 users.

60% use the free plan.
Of free-plan users, 8% convert to paid each month.
Paid users have a 4% monthly churn rate.
No new users join.
Conversion happens before churn each month.
A converted user cannot churn during the same month they convert.

Question: After one month, how many free users and paid users are expected to remain?

Show the calculation clearly. Do not round intermediate values.

Output format: { "free_users_after_month_1": number, "paid_users_after_month_1": number, "calculation": ["...", "...", "..."], "assumptions": ["..."] }

Candidate — anthropic/claude-opus-5

done

{
  "free_users_after_month_1": 552,
  "paid_users_after_month_1": 432,
  "calculation": [
    "Starting split: free = 1,000 × 60% = 600; paid = 1,000 − 600 = 400",
    "Step 1 — Conversion: 600 × 8% = 48 free users convert to paid",
    "Free users remaining: 600 − 48 = 552",
    "Step 2 — Churn (applies only to the 400 pre-existing paid users, since new converts are exempt this month): 400 × 4% = 16 churned",
    "Paid users: 400 − 16 + 48 = 432",
    "Check on total: 552 + 432 = 984 = 1,000 − 16 churned users"
  ],
  "assumptions": [
    "Churned users leave the product entirely (they do not revert to the free plan); this is why the total drops from 1,000 to 984.",
    "The 4% churn rate applies to the paid base at the start of the month (400), excluding the 48 same-month converts, per the stated rule.",
    "No new signups, no downgrades other than churn, and no free-user attrition.",
    "Values are expected values; all figures happen to be whole numbers, so no rounding was needed."
  ]
}

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Judges

median 10.0

gpt-5.6-solscored

PASS10.0

grok-4.5scored

PASS10.0

gemini-3.1-pro-previewscored

PASS10.0

8/8 checks passed

Output parses as JSON
expected "valid JSON object" · got "parsed"
No prose outside the JSON object
expected "JSON only (optional single fence)" · got "clean"
All required keys present
expected ["free_users_after_month_1","paid_users_after_month_1","calculation","assumptions"] · got ["free_users_after_month_1","paid_users_after_month_1","calculation","assumptions"]
Values have the expected types
expected {"free_users_after_month_1":"number","paid_users_after_month_1":"number","calculation":"array","assumptions":"array"} · got {"free_users_after_month_1":"number","paid_users_after_month_1":"number","calculation":"array","assumptions":"array"}
Arrays have the exact required counts
expected {} · got {}
Free-plan count present as an integer
expected 552 · got 552
Paid-plan count present as an integer
expected 432 · got 432
Exact answers — free = 552, paid = 432
expected {"free":552,"paid":432} · got {"free":552,"paid":432}

Loading cell…

{ "free_users_after_month_1": 552, "paid_users_after_month_1": 432, "calculation": [ "Starting split: free = 1,000 × 60% = 600; paid = 1,000 − 600 = 400", "Step 1 — Conversion: 600 × 8% = 48 free users convert to paid", "Free users remaining: 600 − 48 = 552", "Step 2 — Churn (applies only to the 400 pre-existing paid users, since new converts are exempt this month): 400 × 4% = 16 churned", "Paid users: 400 − 16 + 48 = 432", "Check on total: 552 + 432 = 984 = 1,000 − 16 churned users" ], "assumptions": [ "Churned users leave the product entirely (they do not revert to the free plan); this is why the total drops from 1,000 to 984.", "The 4% churn rate applies to the paid base at the start of the month (400), excluding the 48 same-month converts, per the stated rule.", "No new signups, no downgrades other than churn, and no free-user attrition.", "Values are expected values; all figures happen to be whole numbers, so no rounding was needed." ] }