The cube, 41063625 ( \(345^3\) ), can be permuted to produce two other cubes: 56623104 ( \(384^3\) ) and 66430125 ( \(405^3\) ). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.
Find the smallest cube for which exactly five permutations of its digits are cube.
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
| Triangle | \(P_{3,n}=n(n+1)/2\) | 1, 3, 6, 10, 15, … |
| Square | \(P_{4,n}=n2\) | 1, 4, 9, 16, 25, … |
| Pentagonal | \(P_{5,n}=n(3n−1)/2\) | 1, 5, 12, 22, 35, … |
| Hexagonal | \(P_{6,n}=n(2n−1)\) | 1, 6, 15, 28, 45, … |
| Heptagonal | \(P_{7,n}=n(5n−3)/2\) | 1, 7, 18, 34, 55, … |
| Octagonal | \(P_{8,n}=n(3n−2)\) | 1, 8, 21, 40, 65, … |
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
- The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
- Each polygonal type: triangle (\(P_{3,127}=8128\)), square (\(P_{4,91}=8281\)), and pentagonal (\(P_{5,44}=2882\)), is represented by a different number in the set.
- This is the only set of 4-digit numbers with this property.
Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.
The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.
Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.
很久以前做过一个ASCII艺术代码，是python版本的。当时在django的架构下跑。自从换了Github Page就不能用了。这几天终于抽空用javascript重构了一下。
芒芒芒
芒连满相暑相夏满连 芒满满
满暑相夏满夏夏 芒连满夏相暑相夏满连
连连 芒 芒芒芒相连
芒连夏满满满夏暑连 芒相芒
夏芒 芒 芒相芒 夏芒 连
满夏夏满连 芒夏 满连 连暑连
连连 连满芒芒满 夏满芒芒连满夏夏暑芒
芒连芒 芒满 芒暑暑暑相满芒 连芒
芒连连满夏夏相芒 芒满芒 夏满
芒相连 连满
满满 连满夏芒 连满芒满满
芒满芒芒 相满 连满夏相暑相满满芒
芒夏连连 连夏 芒芒 连连
芒夏芒 满满夏芒 连连
芒满 芒相相连 满夏满满相相暑暑夏芒
芒 满夏芒芒相夏芒 芒相相相相相夏满连芒芒芒 芒连芒
芒满夏连 夏暑相连 芒芒
连相暑相夏连
赞服地铁
赞服是我最近一段时间在玩的Minecraft的一个服务器。这个服务器的一大特色就是从来不换周目，于是就造就了很多虽然说不上壮观但是很有意思的……工程。其中一个工程就是地铁系统。虽然没有一些视频里面那种很壮观漂亮的地铁站，但是……
截止到目前为止，赞服地铁一共有39条线路，共计135个地铁站:trollface:。
说数字可能还没什么概念，于是上个图吧。
这个不是我造的，是其他小伙伴的杰作！
抽空做了一个很小很小的修改，但是这个功能以前设想了很久。
就是把一些显示时间的地方改成“X天前”“X年前”。
现成有很多很多的js库都可以做到。但是实际上，只要那么几行就行了。
稍微翻了一下记录，发现这个更新我整整做了一年。
其实比较早的版本早就上线了，但是各种细节处理都没有做的很令我满意。
起因就是，评论系统这个用得非常少但是“如果没有的话又觉得哪里不对”的功能，的支持框架，野狗，翘了~
