Add all the natural numbers below one thousand that are multiples of 3 or 5.

163126

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

135250

Find the largest prime factor of a composite number.

98411

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

91082

What is the smallest number divisible by each of the numbers 1 to 20?

102658

What is the difference between the sum of the squares and the square of the sums?

104509

Find the 10001st prime.

87526

Discover the largest product of five consecutive digits in the 1000-digit number.

77536

Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.

77447

Calculate the sum of all the primes below two million.

70345

What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid?

53531

What is the value of the first triangle number to have over five hundred divisors?

46938

Find the first ten digits of the sum of one-hundred 50-digit numbers.

53386

Find the longest sequence using a starting number under one million.

51471

Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?

42050

What is the sum of the digits of the number 2¹⁰⁰⁰?

56764

How many letters would be needed to write all the numbers in words from 1 to 1000?

35276

Find the maximum sum travelling from the top of the triangle to the base.

35873

How many Sundays fell on the first of the month during the twentieth century?

32748

Find the sum of digits in 100!

54458

Evaluate the sum of all amicable pairs under 10000.

35739

What is the total of all the name scores in the file of first names?

33604

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

23982

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

29211

What is the first term in the Fibonacci sequence to contain 1000 digits?

40924

Find the value of d < 1000 for which 1/d contains the longest recurring cycle.

20266

Find a quadratic formula that produces the maximum number of primes for consecutive values of n.

21411

What is the sum of both diagonals in a 1001 by 1001 spiral?

31536

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

26791

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

29257

Investigating combinations of English currency denominations.

19915

Find the sum of all numbers that can be written as pandigital products.

17159

Discover all the fractions with an unorthodox cancelling method.

18673

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

25650

How many circular primes are there below one million?

23236

Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2.

25754

Find the sum of all eleven primes that are both truncatable from left to right and right to left.

19231

What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ?

15826

If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions?

18896

Finding the n^th digit of the fractional part of the irrational number.

22049

What is the largest n-digit pandigital prime that exists?

17752

How many triangle words does the list of common English words contain?

21498

Find the sum of all pandigital numbers with an unusual sub-string divisibility property.

14365

Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.

13883

After 40755, what is the next triangle number that is also pentagonal and hexagonal?

20455

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

14504

Find the first four consecutive integers to have four distinct primes factors.

14729

Find the last ten digits of 1¹ + 2² + ... + 1000¹⁰⁰⁰.

36365

Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.

14090

Which prime, below one-million, can be written as the sum of the most consecutive primes?

15349