freeCodeCamp/problem-88-product-sum-numbers.md at 13e7251ed9d1fb914bcc68cc0597e364638488d2

Oliver Eyton-Williams 2b9e38a17b

fix: replace .english.md extension with .md

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id, challengeType, title, forumTopicId

id	challengeType	title	forumTopicId
5900f3c51000cf542c50fed6	5	Problem 88: Product-sum numbers	302203

Description

A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a₁, a₂, ... , a_k} is called a product-sum number: N = a₁ + a₂ + ... + a_k = a₁ × a₂ × ... × a_k.

For example, 6 = 1 + 2 + 3 = 1 × 2 × 3.

For a given set of size, k, we shall call the smallest N with this property a minimal product-sum number. The minimal product-sum numbers for sets of size, k = 2, 3, 4, 5, and 6 are as follows.

k=2: 4 = 2 × 2 = 2 + 2
k=3: 6 = 1 × 2 × 3 = 1 + 2 + 3
k=4: 8 = 1 × 1 × 2 × 4 = 1 + 1 + 2 + 4
k=5: 8 = 1 × 1 × 2 × 2 × 2 = 1 + 1 + 2 + 2 + 2
k=6: 12 = 1 × 1 × 1 × 1 × 2 × 6 = 1 + 1 + 1 + 1 + 2 + 6

Hence for 2≤k≤6, the sum of all the minimal product-sum numbers is 4+6+8+12 = 30; note that 8 is only counted once in the sum.

In fact, as the complete set of minimal product-sum numbers for 2≤k≤12 is {4, 6, 8, 12, 15, 16}, the sum is 61.

What is the sum of all the minimal product-sum numbers for 2≤k≤12000?

Instructions

Tests

tests:
  - text: <code>productSumNumbers()</code> should return a number.
    testString: assert(typeof productSumNumbers() === 'number');
  - text: <code>productSumNumbers()</code> should return 7587457.
    testString: assert.strictEqual(productSumNumbers(), 7587457);

Challenge Seed

function productSumNumbers() {

  return true;
}

productSumNumbers();

Solution

// solution required

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