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?
Answer:
Matt: 1 Apple
James: 2 Apples
Ian: 3 Apples
Barry: 5 Apples
The Logic
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?
Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word. How to write better comments?
6 comments
Had not heard this puzzle before.. interesting..
Thank you dear. Glad it puzzled you. 🙂
great post 🙂
Wow! I’m impressed. I’m not at all mathematically inclined. I’m an artist and rather flakey when it comes to numbers.
Interesting! There may be more than one answer but the nearest probability is this one.
The first worthy comment on this topic. Actually the point, I assumed, that one will ask a question, whose answer he doesn’t know, makes the logic and provides the answer. Other answers might be possible- but As I said, it is inspired by a childhood heard puzzle, I thought not to make more changes than original. Thanks for your comment.