"I don't know the numbers": a math puzzle

puzzle.rb

# My solution to a cool math puzzle


# Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told 
# the sum of the numbers, while Peter is told the product of the numbers.

# Then, this dialog occurs between Sandy and Peter:

# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.
# Peter: I don’t know the numbers.
# Sandy: I don’t know the numbers.

# Peter: I do know the numbers.

# What are the numbers?


sum_map = {}
product_map = {}

(1..99).to_a.each do |a|
    (a..99).to_a.each do |b|
        sum_map[a+b] ||= []
        sum_map[a+b] << [a,b]

        product_map[a*b] ||= []
        product_map[a*b] << [a,b]
    end
end

7.times do
    # Peter says I don't know
    # Which means Product is a number which has multiple factorizations
    # We can delete from map those with unique factorization
    product_map.select { |k,v| v.size == 1 }.each do |product,v|
        f = v.first # cannot be a candidate
        product_map = product_map.except(product)

        # the pair f is not a valid candidate so should be removed from a+b's possible partitions
        sum_map[f.first + f.last].reject! { |p| p == f}
        sum_map.reject! { |p| p == (f.first + f.last) && sum_map[f.first + f.last].empty? }
    end

    # Sandy says I don't know
    # Which means Sum is a number which has multiple partitions
    # We can delete from map those with unique partition
    sum_map.select { |k,v| v.size == 1 }.each do |sum,v|
        pt = v.first # cannot be a candidate
        sum_map = sum_map.except(sum)

        # the pair pt is not a valid candidate so should be removed from a+b's possible partitions
        product_map[pt.first * pt.last].reject! { |f| f == pt}
        product_map.reject! { |p| p == (pt.first * pt.last) && product_map[pt.first * pt.last].empty? }
    end
end

puts product_map.select { |k,v| v.size == 1 }.first.last