logicians.rb

# Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100.
# S is given the value x+y and P is given the value xy.  They then have the following conversation.
# P:  I cannot determine the two numbers.
# S:  I knew that.
# P:  Now I can determine them.
# S:  So can I.
# Given that the above statements are true, what are the two numbers?
require 'prime'
check_sum = ->(x) { (2..x / 2).any? { |a| Prime.prime?(a) && Prime.prime?(x - a) }}
build_variation = ->(x) { (2..x / 2).map { |a| [a * (x - a), x, a] }}
variations = (6..99).reject(&check_sum).flat_map(&build_variation)
variations.select! { |x| variations.count { |y| x[0] == y[0] } == 1 }
variations.select! { |x| variations.count { |y| x[1] == y[1] } == 1 }