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INDEX
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INDEX
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Problem 1
Add all the natural numbers below one thousand that are multiples of 3 or 5.
Problem 2
Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
Problem 3
Find the largest prime factor of a composite number.
Problem 4
Find the largest palindrome made from the product of two 3-digit numbers.
Problem 5
What is the smallest number divisible by each of the numbers 1 to 20?
Problem 6
What is the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum?
Problem 7
Find the 10001st prime.
Problem 8
Discover the largest product of five consecutive digits in the 1000-digit number.
Problem 9
Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
Problem 10
Calculate the sum of all the primes below two million.
Problem 11
What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?
Problem 12
What is the value of the first triangle number to have over five hundred divisors?
Problem 13
Find the first ten digits of the sum of one-hundred 50-digit numbers.
Problem 14
Find the longest sequence using a starting number under one million.
Problem 15
Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?
Problem 16
What is the sum of the digits of the number 21000?
Problem 17
How many letters would be needed to write all the numbers in words from 1 to 1000?
Problem 18
Find the maximum sum traveling from the top of the triangle to the base.
Problem 19
How many Sundays fell on the first of the month during the twentieth century?
Problem 20
Find the sum of digits in 100!
Problem 21
Evaluate the sum of all amicable pairs under 10000.
Problem 22
What is the total of all the name scores in the file of first names?
Problem 23
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
Problem 24
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
Problem 25
What is the first term in the Fibonacci sequence to contain 1000 digits?
Problem 26
Find the value of d < 1000 for which 1/d contains the longest recurring cycle.
Problem 27
Find a quadratic formula that produces the maximum number of primes for consecutive values of n.
Problem 28
What is the sum of both diagonals in a 1001 by 1001 spiral?
Problem 29
How many distinct terms are in the sequence generated by ab for 2 <= a <= 100 and 2 <= b <= 100?
Problem 30
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
Problem 31
Investigating combinations of English currency denominations.
Problem 32
Find the sum of all numbers that can be written as pandigital products.
Problem 33
Discover all the fractions with an unorthodox cancelling method.
To be continued...