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Solving problems in different disciplines (computer science, mathematics, physics, natural languages, ...)enKnud van EedenKnud van Eeden(c) Knud van Eeden 2006-2008Wed, 14 September 2008 20:56:00 GMTKnud van EedenMathematics + computer science: Project Euler: Problem: 1: Number theory: Sum of all natural numbers below 1000 that are multiples of 3 or 5If 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
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Sun, 14 September 2008 17:59:00 GMTMathematics + computer science: Project Euler: Problem: 2: Number theory: Sum of all the even-valued terms in the Fibonacci sequence which do not exceed four millionEach 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
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Mon, 15 September 2008 04:43:00 GMTMathematics + computer science: Project Euler: Problem: 3: Number theory: What is the largest prime factor of the number 600851475143?The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143?
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Sun, 16 September 2008 03:08:00 GMTMathematics + computer science: Project Euler: Problem: 4: Number theory: Find the largest palindrome made from the product of two 3-digit numbersA 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
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Sun, 16 September 2008 05:34:00 GMTMathematics + computer science: Project Euler: Problem: 5: Smallest number divisible by all of the numbers from 1 to 20?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?
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Sun, 19 October 2008 21:40:00 GMTMathematics + computer science: Project Euler: Problem: 6: What is the difference between the sum of the squares and the square of the sums?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
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Sun, 19 October 2008 22:54:00 GMTMathematics + computer science: Project Euler: Problem: 7: What is the 10001st prime number?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?
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Sun, 19 October 2008 23:04:00 GMTMathematics + computer science: Project Euler: Problem: 8: Find the greatest product of five consecutive digits in the 1000-digit numberFind the greatest product of five consecutive digits in the 1000-digit number
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Sun, 19 October 2008 23:41:00 GMTMathematics + computer science: Project Euler: Problem: 9: Find the Pythagorean triplet for which a + b + c = 1000. Find the product abc.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.
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Mon, 20 October 2008 01:26:00 GMTMathematics + computer science: Project Euler: Problem: 10: Calculate the sum of all the primes below two million.The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million.
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Mon, 20 October 2008 18:54:00 GMTMathematics + computer science: Project Euler: Problem: 40: An irrational decimal fraction is created by concatenating the positive integersAn 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
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Sun, 19 October 2008 23:43:00 GMTMathematics + computer science: Project Euler: Problem: 46: Number theory: Composite number: Sum prime and twice a squareGet smallest odd composite number that can be written as the sum of a prime and twice a square
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Sun, 14 September 2008 00:59:00 GMTMathematics + computer science: Project Euler: Problem: 49: Number theory: Arithmetic sequence: Tree digit permutated numbers with fixed differenceThe 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?
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Sun, 19 October 2008 21:18:00 GMT