diff --git a/Project-Euler/Problem053.js b/Project-Euler/Problem053.js
new file mode 100644
index 0000000000..cb566eeb03
--- /dev/null
+++ b/Project-Euler/Problem053.js
@@ -0,0 +1,45 @@
+/**
+// https://projecteuler.net/problem=53
+There are exactly ten ways of selecting three from five, 12345:
+123, 124, 125, 134, 135, 145, 234, 235, 245, 345
+In combinatorics, we use the notation, 5C3 = 10
+In general, nCr = n!/(r!(n-r)!), where r <= n +n! = n*(n-1)*...*3*2*1, and 0! = 1 +It is not until n=23, that a value exceeds one-million: 23C10 = 1144066 +How many, not necessarily distinct, value of nCr for 1 <= n <= 100 are greater than one-million? +*/ +export const answer = (minVal, maxVal) => {
+ /*
+ When n is fixed, the maximum value of nCr is when r is the closes to n/2.
+ //Since nCr = nC(n-r), loop from the ceil of n/2 and increase by one until
+ the value becomes less than or equal to one million. Then, multiply by two
+ because of symmetry, but if n is even, then subtract one to avoid overcounting.
+ */
+ var factorials = [1];
+ var maxR = 0;
+ var numWork = 0;
+ var totalNumWork = 0;
+ for (var i=1;i<=maxval;i++){ + factorials.push(factorials[factorials.length-1]*i); + } + for (var n=minVal;n<=maxval;n++){ + maxR = Math.ceil(n/2); + numWork = 0; + for (var r=maxR;r<=n;r++){ + if (factorials[n]/(factorials[r]*factorials[n-r])> 1000000){
+ numWork++;
+ }
+ else{
+ break;
+ }
+ }
+ if (n%2 == 1){
+ numWork = 2*numWork;
+ }
+ else{
+ numWork = Math.max(0, 2*numWork-1);
+ }
+ totalNumWork += numWork;
+ }
+ return totalNumWork
+}
diff --git a/Project-Euler/test/Problem053.test.js b/Project-Euler/test/Problem053.test.js
new file mode 100644
index 0000000000..e66c308745
--- /dev/null
+++ b/Project-Euler/test/Problem053.test.js
@@ -0,0 +1,10 @@
+import { answer } from '../Problem053.js'
+
+describe('Number of values of nCr that exceed 1 million when n is in a certain range', () => {
+ test('range is 10 to 100', () => {
+ expect(answer(10,100)).toBe(4075)
+ })
+ test('range is 1 to 150', () => {
+ expect(answer(1,150)).toBe(10000)
+ })
+})
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