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Problem 32: Pandigital products

curriculum/challenges/english/blocks/project-euler-problems-1-to-100/5900f38c1000cf542c50fe9f.md

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--description--

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital.

Hint: Some products can be obtained in more than one way so be sure to only include it once in your sum.

--hints--

pandigitalProducts(4) should return a number.

js
assert(typeof pandigitalProducts(4) === 'number');

pandigitalProducts(4) should return 12.

js
assert.strictEqual(pandigitalProducts(4), 12);

pandigitalProducts(6) should return 162.

js
assert.strictEqual(pandigitalProducts(6), 162);

pandigitalProducts(7) should return 0.

js
assert.strictEqual(pandigitalProducts(7), 0);

pandigitalProducts(8) should return 13458.

js
assert.strictEqual(pandigitalProducts(8), 13458);

pandigitalProducts(9) should return 45228.

js
assert.strictEqual(pandigitalProducts(9), 45228);

--seed--

--seed-contents--

js
function pandigitalProducts(n) {

  return true;
}

pandigitalProducts(4);

--solutions--

js
// Check for pandigital number
function isPandigital(digitStr) {
  return digitStr
    .split('')
    .sort()
    .every((c, i) => c == i + 1);
}

// Concatenate 3 numbers
function concatenate3Nums(a, b, c) {
  return a.toString() + b.toString() + c.toString();
}

// Find sum of all pandigital products
function pandigitalProducts(n) {
  const products = [];
  let sum = 0;
  const max = Number(Array(n)
    .fill(0)
    .map((_, i) => (n - i).toString())
    .join(''));
  const outerLimit = Math.sqrt(max);

  for (let factor1 = 2; factor1 < outerLimit; factor1++) {
    const innerLimit = max / factor1;

    for (let factor2 = factor1; factor2 < innerLimit; factor2++) {
      const product = factor1 * factor2;
      const concatenated = concatenate3Nums(factor1, factor2, product);

      if (concatenated.length > n) {
        break;
      } else if (concatenated.length == n &&
        isPandigital(concatenated) &&
        !products.includes(product)
      ) {
        products.push(product);
        sum += product;
      }
    }
  }
  return sum;
}