# Digit fifth powers

# Problem 30

# 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 = 94 + 44 + 74 + 44

# As 1 = 14 is not a sum it is not included.

# The sum of these numbers is 1634 + 8208 + 9474 = 19316.

# Find the sum of all the numbers that can be written as the sum of fifth

# powers of their digits.

# Solution by Sam Gerber

# This method returns an array of all the numbers that can be written as the

# sum of nth powers of their digits.

def all_power_digits_sums(n)

max_possible = (9**n) * (n + 1)

results = []

(10..max_possible).each do |number|

results << number if is_power_digit_sum?(number, n)

end

results

end

# This method checks if a number is a sum of the nth powers of its digits

def is_power_digit_sum?(number, n)

return false if number < 10

digits = number.to_s.split("")

number == digits.inject(0){|sum, digit| sum += (digit.to_i)**n}

end

results = all_power_digits_sums(5)

print results

print results.reduce(:+)