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# Curious Number | |
# n-digit number is said to be curious if the last n digits of | |
# its square are the same as the original number. | |
# For example, 25^2 = 625 and 76^2 = 5776. | |
# (Curious numbers are also known as automorphic numbers.) | |
# An example of 9 digit number: | |
# 212890625^2 = 45322418212890625 | |
#Q. Complete the code to return all the curious numbers for n digit | |
#Write a code in following format | |
require 'benchmark' | |
class CuriousNumbers | |
attr_reader :curious_five, :curious_six | |
def initialize(digit) | |
@digit = digit.abs | |
@curious_five = [5] | |
@curious_six = [] | |
end | |
def execute | |
return if @digit < 1 | |
([0,1] + other_curious_numbers).sort.uniq | |
end | |
private | |
def other_curious_numbers | |
ends_with_five | |
ends_with_six | |
curious_five + curious_six | |
end | |
def ends_with_five | |
(2..@digit).each do |num| | |
curious_five << (@curious_five.last**2).to_s[-num..-1].to_i | |
end | |
end | |
def ends_with_six | |
(1..@digit).each do |num| | |
curious_six << (10**num+1) - curious_five[num-1] | |
end | |
end | |
end | |
if __FILE__ == $0 | |
puts CuriousNumbers.new(9).execute | |
end |
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Reference: https://math.stackexchange.com/questions/2714474/how-many-n-digit-automorphic-circular-numbers-are-there