problems.json

[
  {
    "title": "Add all the natural numbers below one thousand that are multiples of 3 or 5.",
    "desc": "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.<p>Find the sum of all the multiples of 3 or 5 below 1000.",
    "result": 233168
  },
  {
    "title": "Find the sum of the even-valued terms in the Fibonacci sequence whose values do not exceed four million.",
    "desc": "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, ...<p>By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.",
    "result": 4613732
  },
  {
    "title": "Find the largest prime factor of a composite number.",
    "desc": "The prime factors of 13195 are 5, 7, 13 and 29.<p>What is the largest prime factor of the number 600851475143?",
    "result": 6857
  },
  {
    "title": "Find the largest palindrome made from the product of two 3-digit numbers.",
    "desc": "A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 &times; 99.<p>Find the largest palindrome made from the product of two 3-digit numbers.",
    "result": 906609
  },
  {
    "title": "What is the smallest number divisible by each of the numbers 1 to 20?",
    "desc": "2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.<p>What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?",
    "result": 232792560
  },
  {
    "title": "What is the difference between the sum of the squares and the square of the sums?",
    "desc": "The sum of the squares of the first ten natural numbers is 1<sup>2</sup> + 2<sup>2</sup> + &hellip; + 10<sup>2</sup> = 385<p>The square of the sum of the first ten natural numbers is (1 + 2 + &hellip; + 10)<sup>2</sup> = 55<sup>2</sup> = 3025<p>Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 &minus; 385 = 2640.<p>Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.",
    "result": 25164150
  },
  {
    "title": "Find the 10001st prime.",
    "desc": "By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.<p>What is the 10001st prime number?",
    "result": 104743
  },
  {
    "title": "Discover the largest product of five consecutive digits in the 1000-digit number.",
    "desc": "Find the greatest product of five consecutive digits in the following 1000-digit number.<pre>73167176531330624919225119674426574742355349194934\n96983520312774506326239578318016984801869478851843\n85861560789112949495459501737958331952853208805511\n12540698747158523863050715693290963295227443043557\n66896648950445244523161731856403098711121722383113\n62229893423380308135336276614282806444486645238749\n30358907296290491560440772390713810515859307960866\n70172427121883998797908792274921901699720888093776\n65727333001053367881220235421809751254540594752243\n52584907711670556013604839586446706324415722155397\n53697817977846174064955149290862569321978468622482\n83972241375657056057490261407972968652414535100474\n82166370484403199890008895243450658541227588666881\n16427171479924442928230863465674813919123162824586\n17866458359124566529476545682848912883142607690042\n24219022671055626321111109370544217506941658960408\n07198403850962455444362981230987879927244284909188\n84580156166097919133875499200524063689912560717606\n05886116467109405077541002256983155200055935729725\n71636269561882670428252483600823257530420752963450</pre>",
    "result": 40824
  }
]