Add solution for Project-Euler Problem15

Project-Euler/Problem015.js

@@ -0,0 +1,17 @@
+// https://projecteuler.net/problem=15
+/* 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 20×20 grid?
+*/
+
+// A lattice path is composed of horizontal and vertical lines that pass through lattice points.
+
+const latticePath = (gridSize) => {
+  let paths
+  for (let i = 1, paths = 1; i <= gridSize; i++) {
+    paths = paths * (gridSize + i) / i
+  }
+  // The total number of paths can be found using the binomial coefficient (b+a)/a.
+  return paths
+}
+console.log(latticePath(20)) // output = 137846528820