acertijo-de-las-edades-de-las-hijas.rb

answers = []
sums = []
72.downto(1).each do |h1|
    72.downto(1).each do |h2|
        72.downto(1).each do |h3|
            if h1 * h2 * h3 == 72
                a = [ h1, h2, h3 ].sort.reverse
                if not answers.include?(a)
                    answers << a
                    sums << a[0] + a[1] + a[2]
                end
            end
        end
    end
end
sums.each_index { |i|
    s = sums[i]
    cs = sums.count(s)
    if cs > 1
        a = answers[i]
        if a.count(a[0]) == 1
            puts "Atilio's daughters ages are #{a[0]}, #{a[1]} and #{a[2]}"
            puts "Because from all the possibilities which multiply 72: #{answers.to_s}"
            puts "And having a look to the sums (e.g.: #{a[0]} + #{a[1]} + #{a[2]} = #{s}) array: #{sums.to_s}"
            puts "Only #{s} is repeated #{cs} times, and in this case the elder daughter doesn't share its age with another"
        end
    end
}

# --- RESULT: ---
# Atilio's daughters ages are 8, 3 and 3
# Because from all the possibilities which multiply 72: [[72, 1, 1], [36, 2, 1], [24, 3, 1], [18, 4, 1], [18, 2, 2], [12, 6, 1], [12, 3, 2], [9, 8, 1], [9, 4, 2], [8, 3, 3], [6, 6, 2], [6, 4, 3]]
# And having a look to the sums (e.g.: 8 + 3 + 3 = 14) array: [74, 39, 28, 23, 22, 19, 17, 18, 15, 14, 14, 13]
# Only 14 is repeated 2 times, and in this case the elder daughter doesn't share its age with another