Exploring the spooky and old barracks at night might not have been a good idea. Walking further when you saw the paintings and statements - Strangers will die. Probably wasn't smart either, but now you are trapped in a room with a big metal door. The door is locked with a passcode out of two numbers. You know that both are whole numbers between one and hundred. and that they are neither one or hundred. Only if you find the numbers you can get free, but if you put in wrong numbers just once, the door will be locked forever! The riddle is written on the wall. Two perfectly intelligent men, Frankie and Pete, are talking to each other. Frankie knows only the product, and Pete only the sum of the numbers. Frankie says, "I cannot tell what the numbers are," and Pete answers, "I already knew you couldn't." Frankie happily tells Pete that he now know the numbers, and Pete notices, "Oh, now I know too!" Your survival depends on that seemingly incomplete information. Can you solve this riddle and tell what the two numbers must be? To think about the riddle, pause the video here. The solution comes in... 3, 2, 1. No doubt, you to enter the scary barrack wasn't very lucky. But in every statement of the riddle is more information. And if we logically break it down, one after another there are only the two needed numbers left. That Frankie who knows the product, can't tell what the two numbers are, means that there are many possible ways to build that product with numbers between one and hundred. For example of the product were twenty, the numbers could be two and ten, or four and five. Because of that, we know that the two numbers cannot both be prime numbers, or else Frankie would already know what they were. That Pete already knew that Frankie can't tell the numbers, means that the sum Pete knows cannot be made by adding together two prime numbers. If that were, he couldn't have been sure that Frankie can't solve it. That means there are only 25 possible sums left which causes that Frankie is able to figure out the two needed numbers. Now we know there's only one set of factors which makes the product and makes one of the possible sums if you add them up. Pete now knows that the product is not out of two prime numbers, and that the numbers have to add up to the sum. This time he only counts the possible products that can be made out of splits from the 25 possible sums. By saying he also knows the numbers now Pete tells us that out of the possible products, there's only one which factors add up to the sum he knows. Now we can just look at all possible products. And there must be exactly one which has only one split in two numbers that add up to one of the 25 possible sums. Out of all possible products only the product 52 has a unique sum when you add the splitted numbers together. This number is 17. Finally we know that the sum is 17, the product is 52, and the two needed numbers are 4 and 13. A great, but very difficult riddle, and next time think twice before entering a scary barracks! Hope you enjoyed the riddle, and see you next time!
