Проект Эйлера. Условия задач 1-10 на английском языке

Задачи проекта Эйлера

Эйлер

1-10

Список всех задач

  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.

  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.
  3. The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 600851475143 ?
  4. A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 х 99.

    Find the largest palindrome made from the product of two 3-digit numbers.

  5. 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  (divisible witn no remainder) by all of the numbers from 1 to 20?

  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.

  7. 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?
  8. Find the greatest product of five consecutive digits in the 1000-digit number.
    73167176531330624919225119674426574742355349194934
    96983520312774506326239578318016984801869478851843
    85861560789112949495459501737958331952853208805511
    12540698747158523863050715693290963295227443043557
    66896648950445244523161731856403098711121722383113
    62229893423380308135336276614282806444486645238749
    30358907296290491560440772390713810515859307960866
    70172427121883998797908792274921901699720888093776
    65727333001053367881220235421809751254540594752243
    52584907711670556013604839586446706324415722155397
    53697817977846174064955149290862569321978468622482
    83972241375657056057490261407972968652414535100474
    82166370484403199890008895243450658541227588666881
    16427171479924442928230863465674813919123162824586
    17866458359124566529476545682848912883142607690042
    24219022671055626321111109370544217506941658960408
    07198403850962455444362981230987879927244284909188
    84580156166097919133875499200524063689912560717606
    05886116467109405077541002256983155200055935729725
    71636269561882670428252483600823257530420752963450
  9. 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.

  10. The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.Find the sum of all the primes below two million.