| ID | Description / Title | Solved By |
|---|
1 | Add all the natural numbers below one thousand that are multiples of 3 or 5. | 247550 |
2 | By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. | 204004 |
3 | Find the largest prime factor of a composite number. | 148387 |
4 | Find the largest palindrome made from the product of two 3-digit numbers. | 136436 |
5 | What is the smallest number divisible by each of the numbers 1 to 20? | 150904 |
6 | What is the difference between the sum of the squares and the square of the sums? | 152252 |
7 | Find the 10001st prime. | 129210 |
8 | Discover the largest product of five consecutive digits in the 1000-digit number. | 114042 |
9 | Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. | 114323 |
10 | Calculate the sum of all the primes below two million. | 103917 |
11 | What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid? | 78343 |
12 | What is the value of the first triangle number to have over five hundred divisors? | 69685 |
13 | Find the first ten digits of the sum of one-hundred 50-digit numbers. | 76212 |
14 | Find the longest sequence using a starting number under one million. | 74270 |
15 | Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner? | 61162 |
16 | What is the sum of the digits of the number 21000? | 80548 |
17 | How many letters would be needed to write all the numbers in words from 1 to 1000? | 51254 |
18 | Find the maximum sum travelling from the top of the triangle to the base. | 51454 |
19 | How many Sundays fell on the first of the month during the twentieth century? | 46863 |
20 | Find the sum of digits in 100! | 76652 |
21 | Evaluate the sum of all amicable pairs under 10000. | 50978 |
22 | What is the total of all the name scores in the file of first names? | 47571 |
23 | Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. | 35125 |
24 | What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? | 41722 |
25 | What is the first term in the Fibonacci sequence to contain 1000 digits? | 56630 |
26 | Find the value of d < 1000 for which 1/d contains the longest recurring cycle. | 29198 |
27 | Find a quadratic formula that produces the maximum number of primes for consecutive values of n. | 30814 |
28 | What is the sum of both diagonals in a 1001 by 1001 spiral? | 43503 |
29 | How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100? | 37542 |
30 | Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. | 40289 |
31 | Investigating combinations of English currency denominations. | 28462 |
32 | Find the sum of all numbers that can be written as pandigital products. | 25019 |
33 | Discover all the fractions with an unorthodox cancelling method. | 26421 |
34 | Find the sum of all numbers which are equal to the sum of the factorial of their digits. | 35549 |
35 | How many circular primes are there below one million? | 32496 |
36 | Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. | 35141 |
37 | Find the sum of all eleven primes that are both truncatable from left to right and right to left. | 27001 |
38 | What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? | 22849 |
39 | If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions? | 26594 |
40 | Finding the nth digit of the fractional part of the irrational number. | 30068 |
41 | What is the largest n-digit pandigital prime that exists? | 24995 |
42 | How many triangle words does the list of common English words contain? | 29533 |
43 | Find the sum of all pandigital numbers with an unusual sub-string divisibility property. | 20549 |
44 | Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal. | 20004 |
45 | After 40755, what is the next triangle number that is also pentagonal and hexagonal? | 28213 |
46 | What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? | 21018 |
47 | Find the first four consecutive integers to have four distinct primes factors. | 20820 |
48 | Find the last ten digits of 11 + 22 + ... + 10001000. | 48924 |
49 | Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other. | 20183 |
50 | Which prime, below one-million, can be written as the sum of the most consecutive primes? | 21852 |
