ThePowerSum

#ThePowerSum 

x = 100
n = 3.0

def solution(x, n)
	answer = 0

	power = 1/n

	sq = x**(1/n)

	sqi = sq.to_i


	aofsquares = []
	for i in 1..sqi
		aofsquares = aofsquares.push(i**n)
	end

	count = aofsquares.count
	sumsa = []


	for i in 1..count
	
		sumsa = []
		comba = aofsquares.combination(i).to_a
		
		sumsa = sumsa.push(comba.map {|s| s.sum})
		sumsa.flatten!
		sumsa.delete_if {|s| s != x}
		answer = answer + sumsa.count
		
	end
	

return answer


end	

puts "The number of ways that #{x} can be expressed as sum of the #{n}th power is #{solution(x, n)}"