freeCodeCamp/curriculum/challenges/espanol/10-coding-interview-prep/project-euler/problem-100-arranged-probability.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f3d01000cf542c50fee3	Problem 100: Arranged probability	1	301724	problem-100-arranged-probability

--description--

Si una caja contiene veintiún discos de colores, compuestos por quince discos azules y seis discos rojos, si dos discos son tomados al azar, podemos ver la probabilidad de tomar dos discos azules.

{P(BB)} = \frac{15}{21}×\frac{14}{20} = \frac{1}{2}

The next such arrangement, for which there is exactly a 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs.

By finding the first arrangement to contain over limit discs in total, determine the number of blue discs that the box would contain.

--hints--

arrangedProbability(20) should return a number.

assert(typeof arrangedProbability(10) === 'number');

arrangedProbability(20) should return 15.

assert.strictEqual(arrangedProbability(20), 15);

arrangedProbability(100) should return 85.

assert.strictEqual(arrangedProbability(100), 85);

arrangedProbability(100000) should return 97513.

assert.strictEqual(arrangedProbability(100000), 97513);

arrangedProbability(1000000000) should return 3822685023.

assert.strictEqual(arrangedProbability(1000000000), 3822685023);

arrangedProbability(1000000000000) should return 756872327473.

assert.strictEqual(arrangedProbability(1000000000000), 756872327473);

--seed--

--seed-contents--

function arrangedProbability(limit) {

  return true;
}

arrangedProbability(20);

--solutions--

function arrangedProbability(limit) {
  // Based on https://www.mathblog.dk/project-euler-100-blue-discs-two-blue/
  let blue = 15;
  let discs = 21;

  while (discs < limit) {
    const nextBlue = 3 * blue + 2 * discs - 2;
    const nextDiscs = 4 * blue + 3 * discs - 3;

    blue = nextBlue;
    discs = nextDiscs;
  }
  return blue;
}