2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f4cb1000cf542c50ffde
|
2020-12-16 07:37:30 +00:00
|
|
|
|
title: 问题351:六角形果园
|
2018-10-10 22:03:03 +00:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
2021-01-13 02:31:00 +00:00
|
|
|
|
dashedName: problem-351-hexagonal-orchards
|
2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --description--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
n阶六角形果园是由正六边形中具有边n的点构成的三角形格子。以下是5阶六角形果园的示例:
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
以绿色突出显示的是通过靠近它的点从中心隐藏的点。可以看出,对于5阶六角形果园,中心隐藏了30个点。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
设H(n)是在n阶六角形果园中从中心隐藏的点数。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
H(5)= 30.H(10)= 138.H(1 000)= 1177848。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
找H(100 000 000)。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --hints--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`euler351()`应该返回11762187201804552。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert.strictEqual(euler351(), 11762187201804552);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2021-01-13 02:31:00 +00:00
|
|
|
|
# --seed--
|
|
|
|
|
|
|
|
|
|
## --seed-contents--
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function euler351() {
|
|
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
euler351();
|
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --solutions--
|
2020-08-13 15:24:35 +00:00
|
|
|
|
|
2021-01-13 02:31:00 +00:00
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|