steloflute

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 211 04 October 2008 For a positive integer n, let σ2(n) be the sum of the squares of its divisors. For example, σ2(10) = 1 + 4 + 25 + 100 = 130. Find the sum of all n, 0 n 64,000,000 such that σ2(n) is a perfect square. Solution in C# Brute force took several hours. using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics; namespace Eule..

Problem 58 05 December 2003 Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 31 38 17 16 15 14 13 30 39 18 5 4 3 12 29 40 19 6 1 2 11 28 41 20 7 8 9 10 27 42 21 22 23 24 25 26 43 44 45 46 47 48 49It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that..

Problem 57 21 November 2003 It is possible to show that the square root of two can be expressed as an infinite continued fraction. 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213... By expanding this for the first four iterations, we get: 1 + 1/2 = 3/2 = 1.5 1 + 1/(2 + 1/2) = 7/5 = 1.4 1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666... 1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379... The next thre..

Problem 56 07 November 2003 A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1. Considering natural numbers of the form, ab, where a, b 100, what is the maximum digital sum? Solution in C# using System; using System.Collections.Generic; ..

Problem 55 24 October 2003 If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. Not all numbers produce palindromes so quickly. For example, 349 + 943 = 1292, 1292 + 2921 = 4213 4213 + 3124 = 7337 That is, 349 took three iterations to arrive at a palindrome. Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that nev..