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 = 1000 × 0.60 = 600; paid = 1000 − 600 = 400",
    "Conversions: 600 × 0.08 = 48 free users convert to paid",
    "Free after conversion: 600 − 48 = 552",
    "Churn base (excludes the 48 just-converted users): 400 existing paid users",
    "Churned paid users: 400 × 0.04 = 16",
    "Paid after month 1: 400 + 48 − 16 = 432",
    "Check total: 552 + 432 = 984 (16 churned users left the product)"
  ],
  "assumptions": [
    "Churned paid users exit the product entirely rather than reverting to the free plan (hence total drops from 1000 to 984); if they returned to free, free would be 568 and paid 432.",
    "Rates are applied deterministically to expected counts, and the initial 60/40 split gives whole numbers, so no rounding was needed.",
    "No new signups, no reactivations, and no free-user cancellations."
  ]
}

Tokens880

Cost$0.0143

Latency7.5s

Finishstop

Judges

median 10.0

deepseek-v4-proscored

PASS10.0

grok-4.5scored

PASS10.0

gemini-3.6-flashscored

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 = 1000 × 0.60 = 600; paid = 1000 − 600 = 400", "Conversions: 600 × 0.08 = 48 free users convert to paid", "Free after conversion: 600 − 48 = 552", "Churn base (excludes the 48 just-converted users): 400 existing paid users", "Churned paid users: 400 × 0.04 = 16", "Paid after month 1: 400 + 48 − 16 = 432", "Check total: 552 + 432 = 984 (16 churned users left the product)" ], "assumptions": [ "Churned paid users exit the product entirely rather than reverting to the free plan (hence total drops from 1000 to 984); if they returned to free, free would be 568 and paid 432.", "Rates are applied deterministically to expected counts, and the initial 60/40 split gives whole numbers, so no rounding was needed.", "No new signups, no reactivations, and no free-user cancellations." ] }