题目链接 原题: It turns out that 12 cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples. 12 cm: (3,4,5)24 cm: (6,8,10)30 cm: (5,12,13)36 cm: (9,12,15)40 cm: (…

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 ×…

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…

本题来自 Project Euler 第5题:https://projecteuler.net/problem=5 # Project Euler: Problem 5: Smallest multiple # 2520 is the smallest number that can be divided by # each of the numbers from 1 to 10 without any remainder. # What is the smallest positive num…

本题来自 Project Euler 第4题:https://projecteuler.net/problem=4 # Project Euler: Problem 4: Largest palindrome product # A palindromic number reads the same both ways. # The largest palindrome made from the product # of two 2-digit numbers is 9009 = 91 × 9…

本题来自 Project Euler 第3题:https://projecteuler.net/problem=3 # Project Euler: Problem 3: Largest prime factor # The prime factors of 13195 are 5, 7, 13 and 29. # What is the largest prime factor of the number 600851475143 ? # Answer: 6857 a = 6008514751…

本题来自 Project Euler 第2题:https://projecteuler.net/problem=2 # Each new term in the Fibonacci sequence is generated # by adding the previous two terms. # By starting with 1 and 2, the first 10 terms will be: # 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... # By…

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…

题目链接 思路: 勾股数组,又称毕达格拉斯三元组. 公式:a = s*t b = (s^2 - t^2) / 2 c = (s^2 + t^2) / 2 s > t >=1 且为互质的奇数 代码: #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi f…

Right triangles with integer coordinates The points P (x1, y1) and Q (x2, y2) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ. There are exactly fourteen triangles containing a right angle that can be formed whe…

Su Doku Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept. Its origin is unclear, but credit must be attributed to Leonhard Euler who invented a similar, and much more difficult, puzzle idea called Latin Squares. T…

Darts In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty. The score of a dart is determined by the number of the region that the dart lands in. A dart landing outs…

Diophantine reciprocals I In the following equation x, y, and n are positive integers. For n = 4 there are exactly three distinct solutions: What is the least value of n for which the number of distinct solutions exceeds one-thousand? NOTE: This prob…

Minimal network The following undirected network consists of seven vertices and twelve edges with a total weight of 243. The same network can be represented by the matrix below.   A B C D E F G A - 16 12 21 - - -   B 16 - - 17 20 - -   C 12 - - 28 -…

Special subset sums: meta-testing Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true: S(B) ≠ S(C); that is, sums of subse…

Special subset sums: optimum Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true: S(B) ≠ S(C); that is, sums of subsets ca…