When is Alice's train?
Alice is getting on a train. The train timetable is written in the hh:mm format (hours and minutes). She tells Bob the hour of her train and Chris the minute of her train.
Here is the train timetable: 13:15, 13:45, 14:12, 15:12, 15:38, 15:57, 16:15, 16:38, 17:57.
The following conversation takes place:
Bob: I don't know the full train time
Chris: I don't know the full train time either
Bob: I know the full train time!
What time is Alice's train?
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1 solution
This list will represent the possibilities of the time of the train.
13:15, 13:45, 14:12, 15:12, 15:38, 15:57, 16:15, 16:38, 17:57
Bob says that he doesn't know the full train time. Because Bob knows the hour of the train, if the hour of the train was unique he would already know the full time. Because he doesn't know the full time, it means we can cross unique hours off the list.
13:15, 13:45, 15:12, 15:38, 15:57, 16:15, 16:38
We can use the same logic for Chris' statement to show that we need to cross off unique minutes of the list.
13:15, 15:38, 16:15, 16:38
Bob knows the full time now so we can reverse the previous logic to show that the hours must be unique.
13:15, 15:38
Either of these two possible times is possible which means that it is impossible to find out which.