# Quickfire Sums

> Timed mental-arithmetic rounds in the browser. Pick a topic and a level, play ten items on their own clocks or a
> 60-second sprint, answer from the keyboard, and get marked instantly. Points reward speed and streaks; personal
> bests are kept per topic, level and clock. A coach model writes fresh item sets for any topic at levels 1-5 and
> debriefs every miss - and the browser re-computes every item it writes before showing it.

URL: https://quickfire-sums.skillsafe.ai/
API: https://quickfire-sums.skillsafe.ai/api.html
Model: gpt-terra (SkillSafe alias; resolves to gpt-5.6-terra), 10% publisher markup
Derived from: @jamesrochabrun/math-teacher (https://skillsafe.ai/skill/@jamesrochabrun/math-teacher/, github.com/jamesrochabrun/skills, MIT)

## What is free (no sign-in)

- The bank: 1,176 items over ten topics x three levels - addition, subtraction, times tables, division, squares and
  roots, percentages, fractions, order of operations, negative numbers, metric units. Each pool is generated
  deterministically from a fixed seed and every item carries a check expression the page's own evaluator verifies.
- Rounds: ten items on per-item clocks (8 s at level 1, 10 s at level 2, 14 s at level 3, longer for word items,
  +2 s for multiple choice) or one 60-second sprint.
- Scoring: 100 points per right answer plus a speed bonus of up to 50, times 1.5 from the 5th right answer in a row
  and 2 from the 10th. Wrong, skipped or timed-out items score 0 and reset the streak.
- Results: an item-by-item grid, a seconds-per-item sparkline, personal bests (score, accuracy, streak, median time
  on right answers), a free replay of just the missed items, CSV and Markdown export.
- History: rounds, bests and decks are kept in this browser and, once signed in, in the account's own collections.
- Two example rounds and two example decks whose coach replies replay at no cost.

## What the coach does (metered, needs sign-in)

One system prompt, two tasks selected by the `task` field of the run input:

- `generate` - a fresh set of 6-20 items for a free-text topic at level 1-5 (`mode: "topic"`), or variants of the
  items just missed (`mode: "misses"`, each item naming the miss it varies in `source_id`). Every item returns a
  `prompt`, an exact `answer`, a `check` expression (digits, + - * / ^, parentheses, sqrt), optional 4 `choices`, a
  one-line `why`. The page evaluates every `check` and rejects any item whose answer disagrees, whose plain-arithmetic
  prompt works out differently, whose choices repeat a value or omit the answer, or which repeats a prompt already
  seen. Rejected items are counted and listed, never shown.
- `debrief` - one card per item the browser recorded as wrong, timed out or skipped: the likely `slip`, the `rule`,
  a `mnemonic` and a `worked` line, plus a headline, a note on pace and next steps. Cards about items that were not
  missed are dropped and counted; misses the reply skipped are named.

Array fields of the run input (`misses`, `avoid`, `round`, `stats`) are JSON strings; the input schema is
scalar-only. Runs carry an Idempotency-Key of the form `quickfire-sums:<task>:<mode>:<inputHash>:a<attempt>`.

## Contract summary

generate reply: {"task":"generate","title":str,"level_label":str,"items":[{"prompt":str,"answer":str,"check":str,"choices":[str x0 or 4],"why":str,"source_id":str}],"notes":[str]}

debrief reply: {"task":"debrief","headline":str,"misses":[{"id":str,"slip":str,"rule":str,"mnemonic":str,"worked":str}],"speed":str,"next":[str]}

## Pages

- / - the app
- /api.html - driving both tasks over HTTP in eight languages, with worked examples
- /llms.txt - this file