freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-301-nim.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4991000cf542c50ffab	Problem 301: Nim	5	301955	problem-301-nim

--description--

Nim is a game played with heaps of stones, where two players take it in turn to remove any number of stones from any heap until no stones remain.

We'll consider the three-heap normal-play version of Nim, which works as follows:

• At the start of the game there are three heaps of stones.
• On his turn the player removes any positive number of stones from any single heap.
• The first player unable to move (because no stones remain) loses.

If (n1,n2,n3) indicates a Nim position consisting of heaps of size n1, n2 and n3 then there is a simple function X(n1,n2,n3) — that you may look up or attempt to deduce for yourself — that returns: zero if, with perfect strategy, the player about to move will eventually lose; or non-zero if, with perfect strategy, the player about to move will eventually win. For example X(1,2,3) = 0 because, no matter what the current player does, his opponent can respond with a move that leaves two heaps of equal size, at which point every move by the current player can be mirrored by his opponent until no stones remain; so the current player loses. To illustrate:

• current player moves to (1,2,1)
• opponent moves to (1,0,1)
• current player moves to (0,0,1)
• opponent moves to (0,0,0), and so wins.

For how many positive integers n ≤ 230 does X(n,2n,3n) = 0 ?

--hints--

euler301() should return 2178309.

assert.strictEqual(euler301(), 2178309);

--seed--

--seed-contents--

function euler301() {

  return true;
}

euler301();

--solutions--

// solution required