摘要：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 numbernis called deficient if the sum of its proper divisors is less tha 阅读全文

摘要：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:012 021 102 120 201 210 阅读全文

摘要：Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:2122 23 242520 78 91019 6 12 1118 54 3121716 15 1413It can be verified that the sum of the numbers on the diagonals is 101.What is the sum of the numbers on the diagonals in a 1001 by 100 阅读全文

摘要：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= 144The 12th term, F12, is the first term to contain three digits.What is the first term in the Fibonacc 阅读全文

摘要：Usingnames.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 na 阅读全文

摘要：You are given the following information, but you may prefer to do some research for yourself.1 Jan 1900 was a Monday.Thirty days has September,April, June and November.All the rest have thirty-one,Saving February alone,Which has twenty-eight, rain or shine.And on leap years, twenty-nine.A leap year 阅读全文

摘要：Let d(n) be defined as the sum of proper divisors ofn(numbers less thannwhich divide evenly inton).If d(a) =band d(b) =a, whereab, thenaandbare an amicable pair and each ofaandbare called amicable numbers.For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefo 阅读全文

摘要：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?1#include<iostream>2usingnamespacestd;34#definenum415longlongPascalTriangle[num][num];67voidCalcPascalTriangle()8{9PascalTriangle[0][ 阅读全文

摘要：The sequence of triangle numbers is generated by adding the natural numbers. So the 7thtriangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...Let us list the factors of the first seven triangle numbers:1: 13: 1,36: 1,2,3,610: 1,2 阅读全文

摘要：The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 600851475143 ?1#include<iostream>2usingnamespacestd;34longlongGetFirstFactor(longlongnum)5{6longlongroot=sqrt((longdouble)num);7for(longlongi=2;i<root;i++)8{9if(num%i==0)10{11returni;12}13}1415retu 阅读全文