steloflute

Problem 10 08 February 2002 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 C# using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace Euler { class Program { static void Main(string[] args) { const long pmax = 2000000; bool[] isPrime = new bool[pmax]; for (long i = 2; i

Problem 9 25 January 2002 A Pythagorean triplet is a set of three natural numbers, a b c, for which, a2 + b2 = c2For example, 32 + 42 = 9 + 16 = 25 = 52.There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. Answer: 31875000 C# using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace Euler9 { class Program { static vo..

Problem 8 11 January 2002 Find the greatest product of five consecutive digits in the 1000-digit number. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444..

Problem 7 28 December 2001 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: 104743 Solution in C# using System; namespace ConsoleApplication1 { class Program { static bool isPrime(int n) { for (int i = 2; i * i

Problem 6 14 December 2001 The sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640. Find the difference between the sum of the squares of the firs..

Problem 5 30 November 2001 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 number that is evenly divisible by all of the numbers from 1 to 20? Answer: 232792560 Solution in C# using System; namespace ConsoleApplication1 { class Program { static void Main(string[] args) { var n = 20; for (var i = 19; i >= 2; ..

Problem 4 16 November 2001 A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99. Find the largest palindrome made from the product of two 3-digit numbers. Answer: 906609 Solution in Perl sub isPalindrome { my ($str) = @_; my $to = length($str) / 2; for ( my $i = 0 ; $i $max); } } } print $max; } problem4(); Python def ..

Problem 3 02 November 2001 The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? Answer: 6857 Solution in Perl my $num = 600851475143; my $p; for ( $p = 2 ; ; $p++ ) { while ( $num % $p == 0 ) { $num /= $p; } last if ( $num num2 1) (loop (add1 p) num2)] [else (display p)]))) ; imperative, one loop #lang racket (define (problem3) (define num..

Problem 2 19 October 2001 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 considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. Answer: 4613732 Solution in Perl use List::Util qw(sum); sub ..

Problem 1 05 October 2001 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. Answer: 233168 Solution in C# using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics; namespace Euler { static class Program { static..