Question: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.
What are the numbers?
Answer: The numbers are 3 and 4.
Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.
Question: I am the first son of my father, I can live without men but men can't live without me, the second son of my father has seen men rise and fall and have all of their secrets in his belly, the third son of my father can never give you his gift forever, he takes it from you when you corrupt it unknowingly but men cry for his gift no matter its cost, the fourth son of my father is an obedient servant in the hands of men but when he losses his master he becomes an unmercifully god, the fifth son of my father is the center of our lives, he guides us but he is a divine mystery. What are we?
Answer: Water, earth, air, fire and spirit.