claude-sonnet-4.6 × math

FAIL3.8

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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-sonnet-4.6

done

{
  "free_users_after_month_1": 552,
  "paid_users_after_month_1": 422,
  "calculation": [
    "Initial free users: 1000 × 0.60 = 600",
    "Initial paid users: 1000 × 0.40 = 400",
    "Free-to-paid conversions: 600 × 0.08 = 48",
    "Free users after conversion: 600 - 48 = 552",
    "Paid users after conversion (before churn): 400 + 48 = 448",
    "Churn applies only to the 400 originally paid users (converted users cannot churn in the same month): 400 × 0.04 = 16",
    "Paid users after churn: 448 - 16 = 432",
    "Wait — re-reading: 'A converted user cannot churn during the same month they convert.' So churn applies only to pre-existing paid users (400), not the 48 newly converted.",
    "Churned paid users: 400 × 0.04 = 16",
    "Final paid users: 400 - 16 + 48 = 432",
    "Final free users: 552"
  ],
  "assumptions": [
    "Initial split: 60% free = 600 users, 40% paid = 400 users",
    "Conversion (8% of free) happens before churn each month, as stated",
    "Churn (4%) applies only to the 400 users who were already on the paid plan at the start of the month; the 48 newly converted users are exempt from churn this month",
    "Churned users leave the system entirely (not counted in either group)",
    "No new users join, as stated"
  ]
}

Correction note: The calculation array contains a self-correction mid-way. The final answers are:

Free users after month 1: 552
Paid users after month 1: 432

{
  "free_users_after_month_1": 552,
  "paid_users_after_month_1": 432,
  "calculation": [
    "Initial free users: 1000 × 0.60 = 600; Initial paid users: 1000 × 0.40 = 400",
    "Conversions from free to paid: 600 × 0.08 = 48

Tokens676

Cost$0.0071

Latency1.7m

Finishstop

Judges

median 3.8

gpt-5.6-solscored

FAIL3.8

grok-4.5scored

FAIL3.8

gemini-3.1-pro-previewscored

FAIL4.0

5/8 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 "prose outside JSON"
prose found outside the JSON document
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 422
expected paid=432, got 422
Exact answers — free = 552, paid = 432
expected {"free":552,"paid":432} · got {"free":552,"paid":422}
expected free=552 paid=432

Loading cell…

{ "free_users_after_month_1": 552, "paid_users_after_month_1": 422, "calculation": [ "Initial free users: 1000 × 0.60 = 600", "Initial paid users: 1000 × 0.40 = 400", "Free-to-paid conversions: 600 × 0.08 = 48", "Free users after conversion: 600 - 48 = 552", "Paid users after conversion (before churn): 400 + 48 = 448", "Churn applies only to the 400 originally paid users (converted users cannot churn in the same month): 400 × 0.04 = 16", "Paid users after churn: 448 - 16 = 432", "Wait — re-reading: 'A converted user cannot churn during the same month they convert.' So churn applies only to pre-existing paid users (400), not the 48 newly converted.", "Churned paid users: 400 × 0.04 = 16", "Final paid users: 400 - 16 + 48 = 432", "Final free users: 552" ], "assumptions": [ "Initial split: 60% free = 600 users, 40% paid = 400 users", "Conversion (8% of free) happens before churn each month, as stated", "Churn (4%) applies only to the 400 users who were already on the paid plan at the start of the month; the 48 newly converted users are exempt from churn this month", "Churned users leave the system entirely (not counted in either group)", "No new users join, as stated" ] }

{ "free_users_after_month_1": 552, "paid_users_after_month_1": 432, "calculation": [ "Initial free users: 1000 × 0.60 = 600; Initial paid users: 1000 × 0.40 = 400", "Conversions from free to paid: 600 × 0.08 = 48