steloflute

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 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 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; ..