题意: 将192分别与1.2.3相乘: 192 × 1 = 192192 × 2 = 384192 × 3 = 576 连接这些乘积,我们得到一个1至9全数字的数192384576.我们称192384576为192和(1,2,3)的连接乘积. 同样地,将9分别与1.2.3.4.5相乘,得到1至9全数字的数918273645,即是9和(1,2,3,4,5)的连接乘积. 对于n > 1,所有某个整数和(1,2, - ,n)的连接乘积所构成的数中,最大的1至9全数字的数是多少? /**********…

Pandigital Fibonacci ends The Fibonacci sequence is defined by the recurrence relation: F[n] = F[n-1] + F[n-2], where F[1] = 1 and F[2] = 1. It turns out that F541, which contains 113 digits, is the first Fibonacci number for which the last nine digi…

题目要求是: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. 这个题目提供两种方法来计算. 方法一:采用最笨拙的方式,直接从1到1000,每一个数都去看看是否可以被3或者5整除…

题意:如果一个n位数恰好使用了1至n每个数字各一次,我们就称其为全数字的.例如,2143就是一个4位全数字数,同时它恰好也是一个素数. 最大的全数字的素数是多少? 思路: 最大全排列素数可以从 n = 9 使用 perv_permutation 倒序生成. 当 n = 9 或者 n = 8 时生成的全排列构成的数一定不是素数,因为它一定能被 3 整除,所以从 7 开始枚举. 因为生成的数字太大,所以采用米勒测试判断素数. /************************************…

题意:找出所有形如 39 × 186 = 7254 这种,由 1 - 9,9个数字构成的等式的和,注意相同的积不计算两次 思路:如下面两种方法 方法一:暴力枚举间断点 /************************************************************************* > File Name: euler032.cpp > Author: WArobot > Blog: http://www.cnblogs.com/WArobot/ >…

可以看到数字125874的两倍251748和它有着完全相同的数字,只是顺序不同而已.求一个最小的正整数\(x\),使得\(2x,3x,4x,5x,6x\)都有完全相同的数字. 分析:此题的思路比较直接,可以明显看出个位数肯定不能满足题目的要求,则我们可以从十开始向上搜寻,求出这个数的二至六倍,算出它们字符串对应的集合是否全等.如果六个数的字符串对应的集合完全相同,则其包含的数字全部相同,即为满足题目要求的数.需要注意的是,这里有一个优化的小技巧,考虑到一个数的六倍和它的差异应该是最大的,所以在判…

开始做 Project Euler 的练习题.网站上总共有565题,真是个大题库啊! # Project Euler, Problem 1: Multiples of 3 and 5 # If we list all the natural numbers below 10 # that are multiples of 3 or 5, we get 3, 5, 6 and 9. # The sum of these multiples is 23. # Find the sum of all…

Project Euler: 欧拉计划是一系列挑战数学或者计算机编程问题,解决这些问题需要的不仅仅是数学功底. 启动这一项目的目的在于,为乐于探索的人提供一个钻研其他领域并且学习新知识的平台,将这一平台打造一个有趣和休闲 的环境. 项目主页:https://projecteuler.net 第一题 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we ge…

本题来自 Project Euler 第11题:https://projecteuler.net/problem=11 # Project Euler: Problem 10: Largest product in a grid # In the 20×20 grid below, four numbers along a diagonal line have been marked in red. # The product of these numbers is 26 × 63 × 78 ×…

上一次接触 project euler 还是2011年的事情,做了前三道题,后来被第四题卡住了,前面几题的代码也没有保留下来. 今天试着暴力破解了一下,代码如下: (我大概是第 172,719 个解出这道题的人) program 4 A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.…

题意:三个正整数a + b + c = 1000,a*a + b*b = c*c.求a*b*c. 解法:可以暴力枚举,但是也有数学方法. 首先,a,b,c中肯定有至少一个为偶数,否则和不可能为以上两个等式均不会成立.然后,不可能a,b为奇c为偶,否则a*a%4=1, b*b%4=1, 有(a*a+b*b) %4 = 2,而c*c%4 = 0.也就是说,a和b中至少有一个偶数. 这是勾股数的一个性质,a,b中至少有一个偶数. 然后,解决过程见下(来自project euler的讨论): tag:m…

CHAPTER 38 Reading ‘the Book of Life’ The Human Genome Project 第38章 阅读生命之书 人体基因组计划 Humans have about 22,000 genes (the exact number is history in the making). How do we know this? Because scientists in laboratories all over the world collaborated on…

In Problem 42 we dealt with triangular problems, in Problem 44 of Project Euler we deal with pentagonal number, I can only wonder if we have to deal with septagonal numbers in Problem 46. Anyway the problem reads Pentagonal numbers are generated by t…

project euler 169 题目链接:https://projecteuler.net/problem=169 参考题解:http://tieba.baidu.com/p/2738022069 #include<bits/stdc++.h> using namespace std; #define fi first #define se second #define mp make_pair #define pb push_back #define rep(i, a, b) for(i…

题目要求是: The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319…

本题来自 Project Euler 第22题:https://projecteuler.net/problem=22 ''' Project Euler: Problem 22: Names scores 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 al…

本题来自 Project Euler 第21题:https://projecteuler.net/problem=21 ''' Project Euler: Problem 21: Amicable numbers 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…

本题来自 Project Euler 第20题:https://projecteuler.net/problem=20 ''' Project Euler: Problem 20: Factorial digit sum n! means n × (n − 1) × ... × 3 × 2 × 1 For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, and the sum of the digits in the number 10! i…

本题来自 Project Euler 第19题:https://projecteuler.net/problem=19 ''' How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)? Answer: 171 ''' from datetime import * firstDay = date(1901,1,1) lastDay = date(…

本题来自 Project Euler 第17题:https://projecteuler.net/problem=17 ''' Project Euler 17: Number letter counts If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. If all th…

本题来自 Project Euler 第16题:https://projecteuler.net/problem=16 ''' Project Euler 16: Power digit sum 2**15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2**1000? Answer: 1366 ''' print(sum(int(i…

本题来自 Project Euler 第15题:https://projecteuler.net/problem=15 ''' Project Euler: Problem 15: Lattice paths Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right…

本题来自 Project Euler 第14题:https://projecteuler.net/problem=14 ''' Project Euler: Problem 14: Longest Collatz sequence The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule…

本题来自 Project Euler 第13题:https://projecteuler.net/problem=13 # Project Euler: Problem 13: Large sum # Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. # Answer: 5537376230 numbers = '''371072875339021027987979982…

本题来自 Project Euler 第12题:https://projecteuler.net/problem=12 # Project Euler: Problem 12: Highly divisible triangular number # The sequence of triangle numbers is generated by adding the natural numbers. # So the 7th triangle number would be 1 + 2 + 3…

本题来自 Project Euler 第10题:https://projecteuler.net/problem=10 # Project Euler: Problem 10: Summation of primes # The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. # Find the sum of all the primes below two million. # Answer: 142913828922 def f(x):…

本题来自 Project Euler 第9题:https://projecteuler.net/problem=9 # Project Euler: Problem 9: Special Pythagorean triplet # A Pythagorean triplet is a set of three natural numbers, # a < b < c, for which, a**2 + b**2 = c**2 # For example, 3**2 + 4**2 = 9 +…

本题来自 Project Euler 第8题:https://projecteuler.net/problem=8 # Project Euler: Problem 8: Largest product in a series # The four adjacent digits in the 1000-digit number # that have the greatest product are 9 × 9 × 8 × 9 = 5832. # Find the thirteen adjac…

本题来自 Project Euler 第7题:https://projecteuler.net/problem=7 # Project Euler: Problem 7: 10001st prime # By listing the first six prime numbers: # 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. # What is the 10 001st prime number? # Answer…

本题来自 Project Euler 第6题:https://projecteuler.net/problem=6 # Project Euler: Problem 6: Sum square difference # The sum of the squares of the first ten natural numbers is, # 1**2 + 2**2 + ... + 10**2 = 385 # The square of the sum of the first ten natur…