The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. Well it’s finally happened and I’ve been forced to sought after more efficient methods of detecting primes. I actually tried running this with a similar piece of code […more]

Feb 26, 2015 |

NewVoxel |

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. Not […more]

Feb 26, 2015 |

NewVoxel |

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450 Find the thirteen adjacent digits in the 1000-digit number that have the […more]

Feb 25, 2015 |

NewVoxel |

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? Oh prime numbers are coming back to bite me in the ass. Came up with a simple solution that is very much similar to Problem 3 […more]

Feb 25, 2015 |

NewVoxel |

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 […more]

Feb 25, 2015 |

NewVoxel |

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? Easiest problem so far with the main concern being figuring out a way to solve […more]

Feb 24, 2015 |

NewVoxel |

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers. Wow wee now we’re getting into some interesting stuff. Can you believe I had to include another library […more]

Feb 24, 2015 |

NewVoxel |

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? This question is a little more difficult than the others. If we had a super computer from the year 3000 we could perform an operation that checks whether every number leading up to […more]

Feb 24, 2015 |

NewVoxel |

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 […more]

Feb 24, 2015 |

NewVoxel |

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. Very simple task that introduces users to some basic loop and conditional […more]