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 alph…

Consider all integer combinations ofabfor 2a5 and 2b5: 22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=3125 If they are then placed in numerical order, with any repeats removed, we get the f…

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 di…

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 d…

Starting in the top left corner of a 22 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner. How many such routes are there through a 2020 grid? 题目大意: 从一个22网格的左上角开始,有6条(不允许往回走)通往右下角的路. 对于2020…

基于Web的企业网和互联网的信息和应用( 1194.22 ) 原文更新日期: 2001年6月21日原文地址: http://www.access-board.gov/sec508/guide/1194.22.htm 这些标准的规范由美国政府提出的制作网页必须遵循的要求.除非这样做会增加过分的负担,否则必须适用这些规定. 符合规范的关键就是严格遵守这些条文.许多机构购买了辅助软件去测试他们的网页.这将有助于人们更加了解这些工具和不同的编码技术之间是如何互相影响的.然而,我们应该始终小心这些 辅助科…

Consider the fraction, n/d, where n and d are positive integers. If nd and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d  8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1…

The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... By converting each letter in a word to a number corresponding to its alphabetical position and…

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime. What is the largest n-digit pandigital prime that exists? 题目大意: 如果一个数字将1到n的每个数字都使用且只…

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relative…