Selected problems from Project Euler
Warning! Solutions are most likely not ideally optimized
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I will make programs more efficient, time allowing
Problem 1 - 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.
Problem 2 - 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. By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
Problem 3 - The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143?
Problem 6 - 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.
Problem 8 - The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.
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Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?