http://www.knudvaneeden.com Solving problems in different disciplines (computer science, mathematics, physics, natural languages, ...) en Knud van Eeden Knud van Eeden (c) Knud van Eeden 2006-2008 Wed, 14 September 2008 20:56:00 GMT Knud van Eeden 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 http://www.knudvaneeden.com/tinyurl.php?urlKey=url000188 Sun, 14 September 2008 17:59:00 GMT 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, ... Find the sum of all the even-valued terms in the sequence which do not exceed four million http://www.knudvaneeden.com/tinyurl.php?urlKey=url000189 Mon, 15 September 2008 04:43:00 GMT The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143? http://www.knudvaneeden.com/tinyurl.php?urlKey=url000190 Sun, 16 September 2008 03:08:00 GMT A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. Find the largest palindrome made from the product of two 3-digit numbers http://www.knudvaneeden.com/tinyurl.php?urlKey=url000191 Sun, 16 September 2008 05:34:00 GMT 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 number that is evenly divisible by all of the numbers from 1 to 20? http://www.knudvaneeden.com/tinyurl.php?urlKey=url000195 Sun, 19 October 2008 21:40:00 GMT 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 first one hundred natural numbers and the square of the sum http://www.knudvaneeden.com/tinyurl.php?urlKey=url000196 Sun, 19 October 2008 22:54:00 GMT 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 10001st prime number? http://www.knudvaneeden.com/tinyurl.php?urlKey=url000197 Sun, 19 October 2008 23:04:00 GMT Find the greatest product of five consecutive digits in the 1000-digit number http://www.knudvaneeden.com/tinyurl.php?urlKey=url000198 Sun, 19 October 2008 23:41:00 GMT A Pythagorean triplet is a set of three natural numbers, a b c, for which, a2 + b2 = c2. For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. http://www.knudvaneeden.com/tinyurl.php?urlKey=url000199 Mon, 20 October 2008 01:26:00 GMT The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. http://www.knudvaneeden.com/tinyurl.php?urlKey=url000200 Mon, 20 October 2008 18:54:00 GMT An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021... It can be seen that the 12th digit of the fractional part is 1. If dn represents the nth digit of the fractional part, find the value of the following expression. If dn represents the nth digit of the fractional part, find the value of the following expression. d1 x d10 x d100 x d1000 x d10000 x d100000 x d1000000 http://www.knudvaneeden.com/tinyurl.php?urlKey=url000192 Sun, 19 October 2008 23:43:00 GMT Get smallest odd composite number that can be written as the sum of a prime and twice a square http://www.knudvaneeden.com/tinyurl.php?urlKey=url000187 Sun, 14 September 2008 00:59:00 GMT 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 sequence. What 12-digit number do you form by concatenating the three terms in this sequence? http://www.knudvaneeden.com/tinyurl.php?urlKey=url000194 Sun, 19 October 2008 21:18:00 GMT