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## Project Euler 30: Digit nth powers – SOLVED

Project Euler 30 Problem Statement Originally published on blog.dreamshire.com, M. Molony, MARCH 30, 2009. Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474...

## Project Euler 31: Coin sums – SOLVED

Project Euler 31 Problem Statement Originally published on blog.dreamshire.com, M. Molony, MARCH 31, 2009. In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2...

## Project Euler 34: Digit factorials – SOLVED

Project Euler 34 Problem Statement 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. Find the sum of all numbers which are equal to the sum of the factorial of their digits. Note: as 1! = 1 and 2! = 2 are not sums they are not included. Solution These...

## Project Euler 35: Circular primes – SOLVED

Project Euler 35 Problem Statement Originally published on blog.dreamshire.com, M. Molony, APRIL 8, 2009. The number 197 is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. There are thirteen such primes below 100:...

## Project Euler 36: Double-base palindromes – SOLVED

Project Euler 36 Problem Statement The decimal number, 585 = 10010010012 (binary), is palindromic in both bases. Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. (Please note that the palindromic number, in either base,...

## Project Euler 37: Truncatable primes – SOLVED

Project Euler 37 Problem Statement Originally published on blog.dreamshire.com, M. Molony, APRIL 23, 2009. The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage:...

## Project Euler 40: Champernowne’s constant – SOLVED

Project Euler 40 Problem Statement An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021… It can be seen that the 12th digit of the fractional part is 1. If dn represents the nth digit of the...

## Project Euler 42: Coded triangle numbers – SOLVED

Project Euler 42 Problem Statement The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, … By converting each letter in a word to a number corresponding to its...

## Project Euler 56: a^b maximum digit sum – SOLVED

Project Euler 56 Problem Statement Considering natural numbers of the form, ab, where a,...

## Project Euler 65: Convergents of e – SOLVED

Project Euler 65 Problem Statement The first ten terms in the sequence of convergents for e are: 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, … The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17. Find the...