steloflute

http://projecteuler.net/problem=61Problem 61 16 January 2004 Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: Triangle P3,n=n(n+1)/2 1, 3, 6, 10, 15, ... Square P4,n=n2 1, 4, 9, 16, 25, ... Pentagonal P5,n=n(3n1)/2 1, 5, 12, 22, 35, ... Hexagonal P6,n=n(2n1) 1, 6, 15, 28, 45, ... Heptagona..

http://www.haskell.org/haskellwiki/Euler_problems

Problem 5410 October 2003 In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:High Card: Highest value card.One Pair: Two cards of the same value.Two Pairs: Two different pairs.Three of a Kind: Three cards of the same value.Straight: All cards are consecutive values.Flush: All cards of the same suit.Full House: Three of a kind and a ..

Problem 52 12 September 2003 It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order. Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. Answer: 142857 C# using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics; namespace Euler { sta..

Problem 51 29 August 2003 By replacing the 1st digit of *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime. By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequent..

Problem 50 15 August 2003 The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a prime below one-hundred. The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953. Which prime, below one-million, can be written as the sum of the most c..

Problem 49 01 August 2003 The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another. There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing seq..

Problem 48 18 July 2003 The series, 11 + 22 + 33 + ... + 1010 = 10405071317. Find the last ten digits of the series, 11 + 22 + 33 + ... + 10001000. Answer: 9110846700 C# using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics; namespace Euler { class Program { static void Main(string[] args) { Console.WriteLine(Enumerable.Range(1, 1000) .Select..

Problem 47 04 July 2003 The first two consecutive numbers to have two distinct prime factors are: 14 = 2 7 15 = 3 5 The first three consecutive numbers to have three distinct prime factors are: 644 = 2² 7 23 645 = 3 5 43 646 = 2 17 19. Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers? Answer: 134043 C# using System; using System.Co..

Problem 46 20 June 2003 It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 9 = 7 + 212 15 = 7 + 222 21 = 3 + 232 25 = 7 + 232 27 = 19 + 222 33 = 31 + 212 It turns out that the conjecture was false. What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? Answer: 5777 C# using Sy..