cats_in_hats.rb

# Write a function which takes a number N of cats and outputs which cats have
# hats. Initially, none of the cats have hats. You walk down the line of cats,
# stopping at every cat, taking off its hat if it has one or putting on a hat
# if it doesn't have one. On the second round, you only stop at every second
# cat [eg #2, #4, #6], on the third round you stop at every third cat [eg #3,
# #6, #9...]. You continue this until you've done as many round as there are
# cats. Your function should output an array containing booleans indicating
# whether each cat has a hat or not by the end.

def cats_in_hats(num_cats)
  cats = []
  1.upto(num_cats) do |m|
    1.upto(num_cats) do |n|
      idx = (m * n) - 1
      next if idx > num_cats
      cats[idx] = cats[idx] ? false : true
    end
  end
  cats
end