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Problem 28

问题描述: Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 2520  7  8  9 1019  6  1  2 1118  5  4  3 1217 16 15 14 13 It can be verified that the sum of the numbers on the diagonals is 101. What is the sum of the numbers o ...

Problem 27

问题描述: Euler published the remarkable quadratic formula: n² + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible b ...

Problem 25

问题描述: The Fibonacci sequence is defined by the recurrence relation: Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1F2 = 1F3 = 2F4 = 3F5 = 5F6 = 8F7 = 13F8 = 21F9 = 34F10 = 55F11 = 89F12 = 144 The 12th term, F12, is the first term to contain three digits. What ...

Problem 24

问题描述: A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are: 012   021   1 ...

Problem 21

问题描述: Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and each of a and b are called amicable numbers. For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, ...

Problem 15

问题描述: Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.   How many routes are there through a 2020 grid?   解决问题: 运用排列组合的知识,问题就是 (m+n)!/(m!*n!)   可以运用动态规划递归解决   public static int find(int a, int b){ if(a<0||b<0){ ...

Problem 13

问题描述: Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 3710728753390210279879799822083759024651013574025046376937677490009712648124896970078050417018260538743249861995247410594742333095130581237266173096299194221336357416157252243056330181107240615490825023067 ...

Problem 16

问题描述: 215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 21000?   解决问题: 大数相乘  
  (一)   如果你只想来个短期旅行 ★建议目的地:韩国济州岛 ★推荐理由:两小时直达韩剧外景天堂 ★签证类型:免签 从地球仪上看,济州岛是国外离上海最近的海岛,从声纳公海出发,55分钟抵达。即使是从北京出发,2小时的航程也比去三亚和香港快得多。更便利的是,只要带着护照和酒店预订单,就可以顺利出关。直线飞行,不转机,飞行时间短,比起飞其他国家需要中转,或动辄十几二十小时的行程,是多么幸福的事。   济州岛比一般的海岛游选择性更多——阳光、沙滩、火山、丛林、牧场、果园,还有大名鼎鼎的泰迪熊博物馆。但这些路线逛起来却非常简单,沿着12号公路线玩下去就可以。这一路上都是韩剧外景天 ...
转载于:http://blog.csdn.net/sharpdew/article/details/763180   最优化原理   1951年美国数学家R.Bellman等人,根据一类多阶段问题的特点,把多阶段决策问题变换为一系列互相联系的单阶段问题,然后逐个加以解决。一些静态模型,只要 ...

problem 23

问题描述: A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number. A number n is called deficient if the sum of its proper divisors ...
 第一课一个男人在他妻子洗完澡后准备进浴室洗澡。这时,门铃响了。妻子迅速用浴巾裹住自己冲到门口。当她打开门时,邻居鲍勃站在那儿。在她开口前,鲍勃说,“你如果把浴巾拿掉,我给你800美元。”想了一会儿,这个 ...

Problem 22

问题描述: Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a nam ...

Problem 18

问题描述: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: 75 95 64 17 47 82 18 35 87 10 20 04 82 ...
主元分析(PCA)理论分析及应用 (主要基于外文教程翻译) 什么是PCA?        PCA是Principal component analysis的缩写,中文翻译为主元分析。它是一种对数据进行分析的技术,最重要的应用是对原有数据进行简化。正如它的名字:主元 ...
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