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id	title	challengeType	forumTopicId	dashedName
5900f3ec1000cf542c50feff	Problem 128: Hexagonal tile differences	5	301755	problem-128-hexagonal-tile-differences

--description--

A hexagonal tile with number 1 is surrounded by a ring of six hexagonal tiles, starting at "12 o'clock" and numbering the tiles 2 to 7 in an anti-clockwise direction.

New rings are added in the same fashion, with the next rings being numbered 8 to 19, 20 to 37, 38 to 61, and so on. The diagram below shows the first three rings.

three first rings of arranged hexagonal tiles with numbers 1 to 37, and with highlighted tiles 8 and 17

By finding the difference between tile n and each of its six neighbours we shall define PD(n) to be the number of those differences which are prime.

For example, working clockwise around tile 8 the differences are 12, 29, 11, 6, 1, and 13. So PD(8) = 3.

In the same way, the differences around tile 17 are 1, 17, 16, 1, 11, and 10, hence PD(17) = 2.

It can be shown that the maximum value of PD(n) is 3.

If all of the tiles for which PD(n) = 3 are listed in ascending order to form a sequence, the 10th tile would be 271.

Find the 2000th tile in this sequence.

--hints--

hexagonalTile() should return 14516824220.

assert.strictEqual(hexagonalTile(), 14516824220);

--seed--

--seed-contents--

function hexagonalTile() {

  return true;
}

hexagonalTile();

--solutions--

// solution required

1.6 KiB Raw Blame History