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: A man lives in an apartment building on the 100th floor. He rides the elevator all the way down to floor 1 every morning then all the way up to floor 100 every evening. The elevator is coin-operated. It costs $0.25 per floor for floors 1-25, $0.50 per floor for floors 26-50, $0.75 per floor for floors 51-75, and $1.00 per floor for floors 75-100. How much money does the man spend each day riding the elevator?
Answer: The man spends $125 per day riding the elevator. It costs $62.50 each way.