2.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3a11000cf542c50feb4 | Problem 53: Combinatoric selections | 5 | 302164 | problem-53-combinatoric-selections |
--description--
There are exactly ten ways of selecting three from five, 12345:
In combinatorics, we use the notation, \\displaystyle \\binom 5 3 = 10
In general, \\displaystyle \\binom n r = \\dfrac{n!}{r!(n-r)!}
, where r \\le n
, n! = n \\times (n-1) \\times ... \\times 3 \\times 2 \\times 1
, and 0! = 1
.
It is not until n = 23
, that a value exceeds one-million: \\displaystyle \\binom {23} {10} = 1144066
.
How many, not necessarily distinct, values of \\displaystyle \\binom n r
for 1 \\le n \\le 100
, are greater than one-million?
--hints--
combinatoricSelections(1000)
should return a number.
assert(typeof combinatoricSelections(1000) === 'number');
combinatoricSelections(1000)
should return 4626.
assert.strictEqual(combinatoricSelections(1000), 4626);
combinatoricSelections(10000)
should return 4431.
assert.strictEqual(combinatoricSelections(10000), 4431);
combinatoricSelections(100000)
should return 4255.
assert.strictEqual(combinatoricSelections(100000), 4255);
combinatoricSelections(1000000)
should return 4075.
assert.strictEqual(combinatoricSelections(1000000), 4075);
--seed--
--seed-contents--
function combinatoricSelections(limit) {
return 1;
}
combinatoricSelections(1000000);
--solutions--
function combinatoricSelections(limit) {
const factorial = n =>
Array.apply(null, { length: n })
.map((_, i) => i + 1)
.reduce((p, c) => p * c, 1);
let result = 0;
const nMax = 100;
for (let n = 1; n <= nMax; n++) {
for (let r = 0; r <= n; r++) {
if (factorial(n) / (factorial(r) * factorial(n - r)) >= limit)
result++;
}
}
return result;
}