Four logicians were having dinner and discussing logical puzzles. After the main course, the waiter brought a large plate that contains 11 slices of cakes. Their debate was intense and in the process, they ended up eating all the cakes. Everyone had at least eaten one cake, and each of them is aware of that fact. Each logician knew how many cakes he ate, but they didn’t have the knowledge of how many cakes each of the others ate.
They had the following conversation to try to find out how many cakes the others ate:
Alex: Did you eat more cakes than I did, Ben?
Ben: I don’t know. Did you eat more cakes than I did, Charles?
Charles: I don’t know.
Danny: I got it!
Danny seemed to find out how many cakes each logician ate solely based on the conversation above. Can you also figure it out?
I tried to give this puzzle to some of my friends who are good at math (a lot better than me) but they were all stumped. Funnily, I asked a waiter, who’s also a friend, and he was able to solve it.
The question looks complicated but it’s actually quite simple if you give it some thoughts.
Since Alex has asked, “Did you eat more cakes than I did, Ben?” it implied that Alex has not eaten 5 cakes or more. If Alex has eaten at least 5 cakes, he would not have asked Ben that question. Ben could not have eaten only one cake since if that’s the case, then he would have known that he hasn’t eaten more than Alex. Of course, Ben also didn’t eat 5 or more so that means that he either ate 2, 3, or 4 cakes. As an excellent logician, Charles has already figured this out. However, he was still not aware whether he ate more cakes than Ben. This means that Charles has eaten either 3 or 4 cakes.
Danny could only deduce how many cakes the others ate if he ate 5 cakes. If he ate, let’s say, 4 cakes, then there would be a lot more possibilities which would make it impossible for him to determine the answer. And the others must have eaten 1, 2 and 3 cakes to add up to 11.
In summary, we can conclude that Alex ate 1, Ben ate 2, Charles ate 3, and Danny ate 5.