freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-438-integer-part-of-polynomial-equations-solutions.english.md

id	challengeType	title	forumTopicId
5900f5231000cf542c510034	5	Problem 438: Integer part of polynomial equation's solutions	302109

Description

For an n-tuple of integers t = (a1, ..., an), let (x1, ..., xn) be the solutions of the polynomial equation xn + a1xn-1 + a2xn-2 + ... + an-1x + an = 0.

Consider the following two conditions: x1, ..., xn are all real. If x1, ..., xn are sorted, ⌊xi⌋ = i for 1 ≤ i ≤ n. (⌊·⌋: floor function.)

In the case of n = 4, there are 12 n-tuples of integers which satisfy both conditions. We define S(t) as the sum of the absolute values of the integers in t. For n = 4 we can verify that ∑S(t) = 2087 for all n-tuples t which satisfy both conditions.

Find ∑S(t) for n = 7.

Instructions

Tests

tests:
  - text: <code>euler438()</code> should return 2046409616809.
    testString: assert.strictEqual(euler438(), 2046409616809);

Challenge Seed

function euler438() {
  // Good luck!
  return true;
}

euler438();

Solution

// solution required