steloflute

Problem 16 03 May 2002 215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 21000? Answer: 1366 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(BigInteger.Pow(2, 1000).ToString().ToCharArray()..

Problem 60 02 January 2004 The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. Find the lowest sum for a set of five primes for which an..

Problem 59 19 December 2003 Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange). For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107. A modern encryption method is to take a text file, convert the bytes to ASCII, then XOR each byte with a given value, taken from a secret key. The advan..

Problem 15 19 April 2002 Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner. How many routes are there through a 2020 grid? Answer: 137846528820 n right moves n down moves choose n down moves out of 2n, where n = 20 40C20 C# using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics; ..

Problem 14 05 April 2002 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 above and starting with 13, we generate the following sequence: 13 40 20 10 5 16 8 4 2 1 It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is tho..

Problem 13 22 March 2002 Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 892616706966236338201363784183..

Problem 12 08 March 2002 The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... Let us list the factors of the first seven triangle numbers: 1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28 We can see that ..

Problem 11 22 February 2002 In the 2020 grid below, four numbers along a diagonal line have been marked in red. 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 2..

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..