freeCodeCamp/curriculum/challenges/portuguese/10-coding-interview-prep/project-euler/problem-15-lattice-paths.md

id	title	challengeType	forumTopicId	dashedName
5900f37b1000cf542c50fe8e	Problem 15: Lattice paths	5	301780	problem-15-lattice-paths

--description--

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a given gridSize?

--hints--

latticePaths(4) should return a number.

assert(typeof latticePaths(4) === 'number');

latticePaths(4) should return 70.

assert.strictEqual(latticePaths(4), 70);

latticePaths(9) should return 48620.

assert.strictEqual(latticePaths(9), 48620);

latticePaths(20) should return 137846528820.

assert.strictEqual(latticePaths(20), 137846528820);

--seed--

--seed-contents--

function latticePaths(gridSize) {

  return true;
}

latticePaths(4);

--solutions--

function latticePaths(gridSize) {
  let paths = 1;

  for (let i = 0; i < gridSize; i++) {
    paths *= (2 * gridSize) - i;
    paths /= i + 1;
  }
  return paths;
}