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id	title	challengeType	forumTopicId	dashedName
5900f4cb1000cf542c50ffde	Problem 351: Hexagonal orchards	5	302011	problem-351-hexagonal-orchards

--description--

A hexagonal orchard of order n is a triangular lattice made up of points within a regular hexagon with side n. The following is an example of a hexagonal orchard of order 5:

hexagonal orchard of order 5, with highlighted in green points, which are hidden from the center by a point closer to it

Highlighted in green are the points which are hidden from the center by a point closer to it. It can be seen that for a hexagonal orchard of order 5, 30 points are hidden from the center.

Let H(n) be the number of points hidden from the center in a hexagonal orchard of order n.

H(5) = 30. H(10) = 138. H(1\\,000) = 1\\,177\\,848.

Find H(100\\,000\\,000).

--hints--

hexagonalOrchards() should return 11762187201804552.

assert.strictEqual(hexagonalOrchards(), 11762187201804552);

--seed--

--seed-contents--

function hexagonalOrchards() {

  return true;
}

hexagonalOrchards();

--solutions--

// solution required

1.3 KiB Raw Blame History