How many apples did each automattician eat?
Four friends Matt, James, Ian and Barry, who all knew each other from being members of the Automattic, called Automatticians, sat around a table that had a dish with 11 apples in it. The chat was intense, and they ended up eating all the apples. Everybody had at least one apple, and everyone know that fact, and each automattician knew the number of apples he ate. They didn’t know how many apples each of the others ate, though. They agreed to ask only questions that they didn’t know the answers to:
Matt asked: Did you eat more apples than I did, James?
James: I don’t know. Did you, Ian, eat more apples than I did?
Ian: I don’t know.
Barry: Aha!! I figured out..
So, Barry figured out how many apples each person ate. Can you do the same?
Matt: 1 Apple
James: 2 Apples
Ian: 3 Apples
Barry: 5 Apples
Matt could not have eaten 5 or more. James could not have eaten only one or he would have known that he hadn’t eaten more than Ian. Neither could he have eaten 5 or more. He could have eaten 2 or 3 or 4 apples. Ian figures this out, although he still doesn’t know if he ate more than James. This mean that Ian must have eaten 3 or 4 apples. Barry can only deduce the other amounts if he ate 5 apples. And the rest, in order to add up to 11 , must have eaten 1, 2 and 3.
Inspired from a childhood heard puzzle.
Related Articles Found on this Blog:
- Fox – Rabbit Chase Problems
- Bicycle Thieves – A puzzle
- Applications of Complex Number Analysis to Divisibility Problems : Two Undergrad Problems
- Number Game: The Word Addition
- A Problem (and Solution) from Bhaskaracharya’s Lilavati
- Six Puzzles
- The Mystery of the Missing Money – A classical puzzle by Human Computer Shakuntala Devi With Solution
- Derivative of x squared is 2x or x ? Where is the fallacy?