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Series
In this loose series I plan to solve the math riddles from the Euler project one by one.
The Task The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. This task is so easy that it is almost not worth its own post. The reason is because it is identical to Task 7, "10001st prime" except...
The Task A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a^2 + b^2 = c^2. For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. Solutio...
The Task The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 8586156078911294949545950173795...
The Task 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? This is a surprisingly tricky one, because the code should execute within one minute according to the P...
The Task The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + 3^3 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + 3 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of the...
The Task 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? Now, the task is calling it "Small...
