Arithmetic Trainer

A Zetamac-style mental-math trainer for quant interviews. Black and white, keyboard first.

▶ Practise now: arithmetictrainer.vercel.app

Open it

• Online: open the link above. Nothing to install.
• Offline: download the repo and double-click index.html. No server, no internet.

How your progress is saved

• By default, in your browser. Every round is saved automatically on your device (localStorage, key arithmeticTrainer.v1). Nothing is sent anywhere. Another browser or device starts empty.
• Signed in (optional, published site only). Settings → Account → enter your email, open the link you receive. Your rounds then sync to your account and appear on every device you sign in on. Sync is local first: you can keep playing offline and it catches up when you're back online.
• Export JSON is still there for a file you keep yourself. See privacy.html.

Back up your data

Settings (S) → Export JSON downloads arithmetic-trainer-YYYY-MM-DD.json. Import JSON shows a preview ("142 rounds, 12 days") and lets you Replace everything or Merge (rounds are matched by id, so merging the same file twice adds nothing). If your last export is older than 7 days, the home screen shows a one-line reminder.

Clearing browser data deletes your history, so export regularly.

Where your data lives

Every round is saved automatically on this computer, inside the browser's own storage (localStorage), not inside this folder. Nothing is sent anywhere.

• Moving or renaming this folder is fine in Chrome and Edge: all local files share one storage there.
• Another browser, another browser profile or a private window starts empty. Export, then Import there.
• Firefox may tie storage to the exact file path, so export before moving the folder if you use it.

Modes (Play screen, keys 1–9 and 0)

#	Mode	What it's for
1	Tables	×÷ (2–12)×(2–12), 60 s. Warm-up; the home screen says "warm-up first" until you play one each day. Once 150 of the 187 table facts have 2+ answers, row 1 becomes Weighted tables (the warm-up from then on) and plain Tables moves to T.
2	Foundations	×÷ (2–12)×(2–100), 60 s. One-digit × two-digit and big divisions (637 ÷ 7).
3	Speed	Zetamac Normal, 60 s.
4	Interview-ready	Zetamac Normal, 120 s: the real benchmark (step 3).
–	Weighted tables	From Review (W), and row 1 of Play after the switch above. Tables, but every × fact and every ÷ (each direction on its own) comes up in proportion to (your median time on it)², so slow facts appear far more often. Facts with no data count as slowest until seen. Counts as the daily warm-up.
5	Weak-fact drill	Shows your top 10 weak facts, then 60 s: ~70% from them (weighted by slowness, with their fact families), ~30% normal Foundations.
6	Interview sim	Optiver-style: 80 questions in 8 min. Integers, decimals, fractions, percentages, estimates. Type and press Enter (0.5, .5, 1/2 all accepted); Tab skips; +1 / −1 (penalty set in Settings) / 0.
7	Custom	Every Zetamac setting: operations, 4 ranges, 30/60/120/300 s. Save named presets.
8	Squares	60 s of squares: 11² to 30² by heart, ending in 5 (65²), near 50 (47²), near 100 (97², 104²). Tab skips a question (no point; it counts as a miss in Review).
9	% and fractions	60 s: percent of a number (15% of 80), swapped percentages (8% of 25 = 25% of 8), fractions as decimals (3 ÷ 8 = 0.375; .375 works too), decimals as fractions (0.375 → 3/8) and adding or subtracting fractions (1/4 + 1/8 → 3/8). A fraction answer gets two boxes: type the numerator, and once it is right the cursor moves to the denominator; no Enter. Answers are in lowest terms (the screen says so under the boxes). Tab skips.
0	Mixed tricks

Modes 8, 9 and 0 are training only: they don't count toward the steps. Each question records which trick it trains (fact key tr-sq5, tr-x11…), so slow tricks show in Review, and a freeze shows the shortcut worked on that exact question ("Ends in 5: 6 × 7 = 42, then 25 → 4225").

In Zetamac modes the answer is accepted the moment it's right; no Enter. A full-length wrong value counts as one wrong attempt (Backspace and keep going). Esc aborts (not saved).

Steps

Step	Mode	Advance when
1	Foundations	day average ≥ 18 for 3 days in a row
2	Speed	day average ≥ 25 for 3 days in a row
3	Interview-ready	day average ≥ 60 for 3 days in a row

A day only counts if it has at least 3 rounds in that step's mode. (In the code and saved data a day of practice is called a session, and the steps keep their old ids P2, P3, P4.) Rounds you enter from zetamac.com (Log screen) count too. Override the step in Settings.

Road to 60 (key C)

A coach for one goal: 60 or more on Normal 120 s. Open Road to 60 in the top bar and press Enter for today's session. The app runs it round by round and, after each round, says what comes next:

Block	Rounds	What
1 Warm-up	1	Tables (Weighted tables once you have passed the switch)
2 Warm-up	2	Foundations
3 Focus A	3	The drill for the category where you lose the most time
4 Focus B	3	The next one (Complements while they are slower than 1.2 s or new)
5 Main	4	Speed (Normal 60 s)
6 Benchmark	2	Normal 120 s: your official score

Every 7th session is a test day: the warm-up, then 4 benchmark rounds, no drills. After block 6 the page says Done for today with a summary; anything you play after that is saved as extra and never counts. Close the tab whenever you like: the session resumes where you were.

• Categories. Every + − × ÷ question gets one: + with or without carry, − with or without borrow, − from 100 or more, × and ÷ tables, and × and ÷ by each number 2–12 with the other factor over 12. Each has a target median (1.0 s for tables up to 2.4 s for big ×).
• Gap to 60. Your median per category (from Foundations, Speed and Normal 120 s, last 3 days, more if a category has under 15 answers), how often Normal asks each one, the estimated score this gives, and the top 5 categories by lost time ("− with borrow: 3.1 s vs 1.9 s target → costs ~4 points").
• Drills (keys 1–5): Complements (37 → 100, and 237 → 240), Carry addition, Borrow subtraction, Cross-100 subtraction, and × ÷ by one number. After 5 seconds on a question a grey line shows the method (never the answer); turn it off in Settings.
• Milestones 40 · 45 · 50 · 55 · 60: reached when your benchmark average is there 2 sessions in a row. 60 counts at 3 in a row.
• Mastered. A category at its target 3 sessions in a row stops being picked as a focus.
• Also on the page: benchmark by time of day, and your warm-up curve (Speed score by round of the day). The report has a Coach section.
• Every end screen of a + − × ÷ round lists answers that took over 8 seconds, with the method.

Screens

The top bar has seven tabs: Play, Learn, Matrices, Finance, Review, Stats and Settings.

• Play (home): the round to play next, big, with one Start button (it follows whatever mode you select with 1–9, 0 or ↑ ↓); then your step as one line with its 3-box streak (open it for the rule and today's count); then all modes. Only one mode is tagged: the warm-up while it is due, then your step's mode.
• End of round: a summary first: score, vs your average over your last 7 days played (and the step threshold), median time vs usual, first-try accuracy, rank among all your rounds in that mode, and up to 3 takeaways (personal best, the operation that cost you most, freezes, a slowdown, wrong attempts). Scroll for the details: seconds per question through the round, answers and median time per third of the clock, each operation vs your usual, time spread, freezes (over 3× your median, with a chunking hint), slowest questions, facts slower or faster than usual, and every question. Buttons and keys: Enter play again, D drill those slow questions, A today’s analysis, H home.
• Learn (N): one lesson per trick (the 14 behind Squares, % and fractions and Mixed tricks), in four groups, each with your status on it. A lesson (#learn/x11) gives the rule, why it works, 3 fresh worked examples and your numbers. Enter practises: 10 questions, no clock, nothing saved; a wrong answer or Tab shows the method under the box, then you type the answer to go on, and the end shows where you needed it. F plays a timed round: 60 s of that trick, saved as mode LEARN and compared only with rounds of the same trick (shown as "Learn: × 11"). Fractions by heart (#learn/fractions): all 49 fractions with a denominator up to 12, plus 1/16, 3/16, 1/20 and 1/25, both ways: 3/7 → type the decimal; 0.429… → type 3/7 in the two boxes. Repeating decimals take 3 places, rounded or cut off (2/3: 0.667 or 0.666); a decimal with … repeats. A grid shows every pair: grey = not seen yet, inverted = slow or often wrong. Practice and timed rounds pick slow and unseen pairs more often (the weighted-tables formula), and the method uses the patterns (ninths, elevenths, sevenths, multiples of 1/d).
• Matrices (X): 2 × 2 matrix products. Choose the entries (ℤ, integers, or ℕ, natural numbers), the range (−9 to 9 by default, −12 to 12, or Custom: your own From and To, between −99 and 99) and the length (60 or 120 s); the choice is remembered. A round shows A × B and four answer boxes: Space goes to the next box (row by row, wrapping), the arrows move anywhere in the grid, and the next matrix comes as soon as all four entries are right. outlines the wrong entries (until you edit them), skips, stops. Each combination of options counts as its own mode ("Matrices, −9 to 9, 60 s") in Log, Progress and the report, so scores are only compared with rounds of the same kind. Saved as mode , questions as op .

Keys

P play · C Road to 60 · N learn · X matrices · Q finance · R review · A stats · S settings · D drill · E G L open the Today, Progress or Log section · T light/dark · ? help. Play: 1–9, 0 or ↑ ↓ select, Enter/Space start. Lesson: Enter practise, F timed round; in practice Tab shows the method. Road to 60: Enter start or continue today's session (once done: an extra round), 1–5 drills. Matrices: Enter start; in a round Space next entry, arrows move, Enter outline wrong entries, Tab skip. Finance: Enter start; sprint H pause and learn (Enter back), Enter checks an estimate, Tab skips; practice Enter check then next, 1–4 choose, S new numbers, C related calculation, Esc done.

Adding a finance template

Templates live in js/finance-templates.js and register with F.register({...}) (fields documented at the top of js/finance-core.js):

1. Give it a stable id (fin.bond.price.3y), a family (arith, quant, fin), a category (the topic shown on the page), a difficulty (1 one formula, round numbers; 2 a constant or two steps; 3 multi-step or a trap).
2. params(rng) draws the inputs from grids with F.pick, F.int, F.grid (realistic, mentally computable values); valid(p) rejects silly draws. Choose the answer first when it should be a clean number.
3. prompt(p), answer(p) (the exact value), unit and dp (decimals shown), tol(p) if not "rounded to dp" (exact, abs, rel: relative tolerances need Enter in a sprint and say "approximately").
4. distractors(p): plausible mistakes computed from the same inputs (the engine drops any within tolerance). steps(p): the formula with the numbers substituted and the intermediate results. Put every formula, letter or symbol between $…$ in the same LaTeX subset ('Discount: $\\text{PV} = \\frac{C}{(1 + r)^t}$.'), in prompts, steps and why too; plain prose and plain numbers stay outside. formula (plain text, used in the report); why. Add the same formula in LaTeX style to the TEX map at the end of the file (\frac{C}{(1 + r)^t}, \sigma_{\text{day}}\sqrt{252}…): js/tex.js draws it as real maths with the browser's MathML. The supported subset is listed at the top of js/tex.js; anything else fails the tests (tests/tex.test.js) and would show the plain formula.
5. Add an independent reference in tests/finance.test.js (REF): a check of the grids and the answer written separately. npm test runs it on 1,000 seeds; npm run samples -- <id> prints examples to read.

Concept questions go in js/finance-bank.js: the right option first (the engine shuffles), a 2–4 sentence explanation, and optionally the id of the calculation to practise next.

How weak facts are found

Each question maps to fact keys: 7x8 for tables (× and ÷ share it), 8x30s and 8x36 for larger ×÷, and add-carry, sub-borrow, add-2d+2d… for + and −. Slowness = median of (time ÷ your median for that operation) × (1 + wrong rate). Attempts older than 21 days count half. A fact is weak with slowness ≥ 1.5 over ≥ 3 attempts, or a stall in the last 2 days: an attempt over 3× your median for that operation (and over 1.5 s), so the bar follows your own pace. Review says "after a freeze" when that stall is the only reason. After a good day (every attempt at or under your median) it is improving. After 3 good days it is mastered. A bad day sends it back to weak.

Develop

Clone the repo and open index.html: there is no build step and the app has no dependencies.

• Progress lives in each person's browser (or their account), never in the repo. Each clone starts empty. Sign-in only works over http(s), not from file://.
• Never commit an export: it is your personal history. .gitignore skips arithmetic-trainer-*.json.
• Tests need Node 18+ and Google Chrome. npm ci installs the exact Playwright and Supabase client versions from package-lock.json (the app itself loads the client from jsDelivr with an integrity hash; tests serve the same file). node_modules/ and test-results/ are not committed.
• Upgrading the Supabase client: change the version and CLIENT_SRI in js/sync.js and in package.json together.
• Keep classic <script> tags (no ES modules, no bundler) so double-clicking index.html keeps working.

Deploy (GitHub → Vercel, accounts with Supabase)

The site is static: Vercel serves the repo as is. vercel.json sets security headers and .vercelignore keeps tests, docs and package.json out of the deploy (so nothing is installed).

1. Vercel: Add New → Project → import the GitHub repo. Framework preset Other, no build command, output directory . (already set by vercel.json). Every push to main deploys; every pull request gets its own preview URL.
2. Put the link where people find it: the URL at the top of this README; set it in the GitHub repo's About → Website box.

Accounts are optional. Without step 3–5 the site works exactly the same, without the Account section.

3. Supabase: create a project (free tier). SQL Editor → paste supabase/schema.sql → Run. It creates the rounds and profiles tables, row-level security (each account sees only its own rows), and the delete_my_account function.
4. Auth settings: Authentication → Sign In / Providers → Email enabled. Authentication → URL Configuration → Site URL = your Vercel URL; Redirect URLs = https://arithmetictrainer.vercel.app/** and https://*-YOUR-TEAM.vercel.app/** (previews).
5. Connect the app: Project Settings → API → copy the project URL and the anon (publishable) key into js/config.js, commit, push. Both values are public by design.

Before sharing widely: Supabase's built-in email sender only allows a few sign-in emails per hour. Set up custom SMTP (Authentication → Emails → SMTP, for example with Resend's free tier).

Tests

Logic (generator, stats, progression, storage) is plain JS with no DOM:

node --test

End-to-end tests drive the real page in your installed Google Chrome with Playwright. Time is mocked (page.clock), so a 60-second round runs in milliseconds. They are a development tool only: the app itself has no dependencies and node_modules is not part of it.

npm ci
npm run test:e2e

They cover: auto-accept, wrong-attempt counting, time-up saving, Esc, Enter to replay, Interview scoring, the home hero, Review views and their URLs, Session deep links and A, Stats sections and old links, the skip link, help, Learn (lessons, practice with the method on a miss, timed rounds saved as LEARN), Matrices, Finance (sprint auto-accept and estimates, practice with worked answers, seed links, intuition keys, the interview mix, saving on leave, progress), zetamac.com entry, export → reset → import, and account sync against a fake Supabase (served over http by tests/e2e/server.js): first sign-in merge, push, tombstones, pull.

Design docs

docs/design.md (tokens), docs/design-guidelines.md (accessibility, copy, do’s and don’ts) and docs/design-components.md (every component) describe the black-and-white system. Copy is sentence case, second person and plain; numbers are monospace with tabular figures.

Files

js/generator.js questions · js/finance-core.js js/finance-templates.js js/finance-bank.js Finance engine, templates, concept questions · js/finance-ui.js Finance tab · js/tex.js LaTeX-subset formulas to MathML · tools/finance-samples.js sample printer (npm run samples, not deployed) · js/lessons.js Learn texts · js/stats.js sessions and weak facts · js/progression.js steps and summary · js/storage.js save/load/export/import · js/sync.js account sync · js/config.js Supabase keys · js/game.js play loop · js/charts.js SVG · js/ui.js screens · js/app.js bootstrap; tests/ logic tests, tests/e2e/ browser tests. Classic <script> tags on one global window.AT (ES modules fail on file://).

License

MIT, see LICENSE.