🧮 @coffeeandfun/maths-captcha

A small Node.js library that generates simple maths questions and checks the answers. Use it as a friendly alternative to image based CAPTCHAs. ✨

Examples of what it can ask:

• 7 + 3
• 25% of 80
• √64
• 2x + 3 = 11
• 2, 4, 6, 8, ?

It runs in plain JavaScript. There are no servers to call, no images to load, and no fonts to download.

---

📦 Install

npm install @coffeeandfun/maths-captcha

Requires Node.js 16 or newer.

---

🚀 Quick start

import {
  generateRandomMathQuestion,
  validateAnswer,
} from '@coffeeandfun/maths-captcha';

const question = generateRandomMathQuestion();
console.log(question.question);
// "7 + 3"

const isCorrect = validateAnswer(question, '10');
console.log(isCorrect);
// true

That's the whole loop: generate a question, show it to the user, then check what they typed.

---

📝 What you get back

Every question is a plain object with the same shape:

{
  question: '7 + 3',     // The text to show the user
  answer: '10',          // The correct answer as a string
  numericAnswer: 10,     // The correct answer as a number
  operation: '+',        // The operator or category
  operands: [7, 3],      // The numbers used to build the question
  type: 'arithmetic',    // Which question type produced it
}

Some types add a style field (for example, square, cube, geometric).

---

🎲 Question types

By default the library only asks basic arithmetic. You can switch on more types when you want harder or more varied questions.

Type	Example	Notes
arithmetic	7 + 3	+ - * / and % (modulo)
power	5^2, √64	Squares, cubes, perfect square roots
percentage	25% of 80	Always whole-number answers
pemdas	(2 + 3) * 4	Order of operations
solve-x	2x + 3 = 11	Solve for x
sequence	2, 4, 6, 8, ?	Arithmetic and geometric patterns

Turn on extra types with setConfig:

import {
  setConfig,
  generateRandomMathQuestion,
} from '@coffeeandfun/maths-captcha';

setConfig({
  QUESTION_TYPES: ['arithmetic', 'power', 'percentage', 'solve-x'],
});

const question = generateRandomMathQuestion();
// e.g. { question: '√64', answer: '8', type: 'power', style: 'sqrt', ... }

---

✅ Checking answers

There are three ways to check an answer. Pick the one that fits how strict you want to be.

validateAnswer(question, userAnswer)

Strict. Whole numbers must be typed as whole numbers.

validateAnswer({ answer: '15' }, '15');    // ✅ true
validateAnswer({ answer: '15' }, '15.0');  // ❌ false
validateAnswer({ answer: '15' }, '16');    // ❌ false

validateAnswerFlexible(question, userAnswer)

Friendly. Accepts the same number written different ways.

const q = { answer: '4.00', numericAnswer: 4, operation: '/' };

validateAnswerFlexible(q, '4');     // ✅ true
validateAnswerFlexible(q, '4.0');   // ✅ true
validateAnswerFlexible(q, '4.00');  // ✅ true
validateAnswerFlexible(q, '3.99');  // ❌ false

validateAnswerWithFeedback(question, userAnswer)

Returns an object that explains the result. Useful when you want to show the user why their answer was wrong.

validateAnswerWithFeedback(question, 'abc');
// {
//   isValid: false,
//   reason: 'Invalid numeric format',
//   userInput: 'abc',
//   expected: '10'
// }

Batch checks

If you have many answers to check at once:

validateAnswers([
  { question: q1, answer: '10' },
  { question: q2, answer: '7' },
]);
// [
//   { question: '5 + 5', isValid: true, expectedAnswer: '10' },
//   { question: '14 - 7', isValid: true, expectedAnswer: '7' },
// ]

---

⚙️ Configuration

import {
  setConfig,
  getConfig,
  resetConfig,
} from '@coffeeandfun/maths-captcha';

setConfig({
  DIVISION_PRECISION: 3,
  NUMBER_RANGE: { min: 1, max: 50 },
  OPERATIONS: ['+', '-', '*'],
  QUESTION_TYPES: ['arithmetic', 'power'],
  AVOID_NEGATIVE_RESULTS: true,
  AVOID_DIVISION_BY_ZERO: true,
});

getConfig();   // Read the current settings
resetConfig(); // Restore the defaults

Default settings

Option	Default
DIVISION_PRECISION	2
NUMBER_RANGE	{ min: 1, max: 100 }
OPERATIONS	['+', '-', '*', '/']
QUESTION_TYPES	['arithmetic']
AVOID_NEGATIVE_RESULTS	true
AVOID_DIVISION_BY_ZERO	true
MAX_ATTEMPTS	10
TOLERANCE	1e-10

Difficulty examples

Easy mode for kids:

setConfig({
  QUESTION_TYPES: ['arithmetic'],
  OPERATIONS: ['+'],
  NUMBER_RANGE: { min: 1, max: 10 },
});

Harder mode for adults:

setConfig({
  QUESTION_TYPES: ['arithmetic', 'pemdas', 'solve-x', 'sequence'],
  NUMBER_RANGE: { min: 1, max: 50 },
});

---

📚 Generating in bulk

import { generateMultipleQuestions } from '@coffeeandfun/maths-captcha';

const ten = generateMultipleQuestions(10);

🎯 Generating with limits

If you need a question that fits specific bounds:

import { generateQuestionWithConstraints } from '@coffeeandfun/maths-captcha';

const easy = generateQuestionWithConstraints({
  operations: ['+'],
  numberRange: { min: 1, max: 10 },
  maxResult: 20,
});

If the library cannot produce a question that fits, it throws. Wrap the call in a try block if you want to handle that.

---

🔌 Adding your own question type

You can plug in your own generator. It just needs to return a question object in the standard shape.

import {
  registerQuestionType,
  setConfig,
  generateRandomMathQuestion,
} from '@coffeeandfun/maths-captcha';

registerQuestionType('double', () => {
  const n = Math.floor(Math.random() * 20) + 1;
  return {
    question: `Double ${n}`,
    answer: String(n * 2),
    numericAnswer: n * 2,
    operation: 'custom',
    operands: [n],
    type: 'double',
  };
});

setConfig({ QUESTION_TYPES: ['double'] });

generateRandomMathQuestion();
// { question: 'Double 7', answer: '14', ... }

To remove it later:

import { unregisterQuestionType } from '@coffeeandfun/maths-captcha';
unregisterQuestionType('double');

To see every type that is currently available:

import { listQuestionTypes } from '@coffeeandfun/maths-captcha';
listQuestionTypes();
// ['arithmetic', 'power', 'percentage', 'pemdas', 'solve-x', 'sequence', 'double']

---

🌐 Using it with Express

Generate the question on the server and store it in the session. Validate the answer on the server too. Never trust the client to check itself.

import express from 'express';
import session from 'express-session';
import {
  generateRandomMathQuestion,
  validateAnswer,
} from '@coffeeandfun/maths-captcha';

const app = express();
app.use(express.json());
app.use(session({
  secret: 'change-me',
  resave: false,
  saveUninitialized: true,
}));

app.get('/captcha', (req, res) => {
  const question = generateRandomMathQuestion();
  req.session.captcha = question;
  res.json({ question: question.question });
});

app.post('/verify', (req, res) => {
  const correct = validateAnswer(req.session.captcha, req.body.answer);
  res.json({ correct });
});

---

📖 API reference

Generators

Function	What it does
generateRandomMathQuestion(precisionOrConfig?)	Returns one question.
generateMultipleQuestions(count, precisionOrConfig?)	Returns an array of questions.
generateQuestionWithConstraints(constraints)	Returns a question that fits the given limits.
registerQuestionType(name, generator)	Adds your own question type.
unregisterQuestionType(name)	Removes a custom question type.
listQuestionTypes()	Lists every available type.

Validators

Function	What it does
validateAnswer(question, answer)	Strict check. Returns true or false.
validateAnswerStrict(question, answer)	The same as validateAnswer. Kept for clarity.
validateAnswerFlexible(question, answer)	Accepts equivalent decimal forms.
validateAnswerWithFeedback(question, a)	Returns an object explaining the result.
validateAnswers(pairs)	Checks many { question, answer } pairs at once.
checkIfSolvedCorrectly(question, answer)	Alias for validateAnswer.

Configuration

Function	What it does
getConfig()	Returns a copy of the current settings.
setConfig(obj)	Merges obj into the active settings.
resetConfig()	Restores the default settings.

Helpers

Function	What it does
getQuestionStats(question)	Returns { operands, result, operation, difficulty, hasDecimals }.
calculateDifficulty(question)	Returns a difficulty score from 1 to 10.
normalizeNumericString(value)	Trims trailing zeros from a numeric string. For example, 5.00 → 5.

---

🧪 Testing

npm test       # Run every test
npm run v1     # Run only the version 1 tests
npm run v2     # Run only the version 2 tests
npm run v3     # Run only the version 3 tests

The library ships with 87 tests covering question generation, every validator, edge cases, and the new question types.

---

⬆️ Upgrading from version 2

Version 3 is a clean rewrite split into small modules. The public API is the same, so existing code keeps working without changes. The new features (extra question types, custom generators, resetConfig) are opt in.

If you only ever called generateRandomMathQuestion and validateAnswer, you do not need to change anything.

---

📄 License

MIT. See LICENSE. 🧡