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id	title	challengeType	forumTopicId	dashedName
5900f45f1000cf542c50ff71	Problem 242: Odd Triplets	5	301889	problem-242-odd-triplets

--description--

Given the set {1,2,..., n}, we define f(n, k) as the number of its k-element subsets with an odd sum of elements. For example, f(5,3) = 4, since the set {1,2,3,4,5} has four 3-element subsets having an odd sum of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.

When all three values n, k and f(n, k) are odd, we say that they make an odd-triplet [n, k, f(n, k)].

There are exactly five odd-triplets with n ≤ 10, namely: [1, 1, f(1, 1) = 1], [5, 1, f(5, 1) = 3], [5, 5, f(5, 5) = 1], [9, 1, f(9, 1) = 5] and [9, 9, f(9, 9) = 1].

How many odd-triplets are there with n ≤ {10}^{12}?

--hints--

oddTriplets() should return 997104142249036700.

assert.strictEqual(oddTriplets(), 997104142249036700);

--seed--

--seed-contents--

function oddTriplets() {

  return true;
}

oddTriplets();

--solutions--

// solution required

1.1 KiB Raw Blame History