Anil is taking a bus to Pune. Anil tells Ali the hour of his bus departure and he tells Alice at which minute it leaves. He also tells them both that the bus leaves between 0600 and 1000.
Ali & Alice consult the timetable and find the following services between those two time: 0632 0643 0650 0717 0746 0819 0832 0917 0919 0950.
Ali then says “I don’t know when Anil’s bus leaves but I am sure that neither does Alice”
Alice replies “I didn’t know his bus, but now I do”
Ali responds “Now I do as well!”
When is Anil’s bus?
Answers
Look at what Ali has to say when asked about Anil's bus timing -
“I don’t know when Anil’s bus leaves but neither does Alice”.
Ali is only aware of the hour at which Anil's bus leaves (i.e. between 0600/0700/0800/0900 hrs). Hence it is confusing for him to find the exact time without knowing the minute. Another point to note; Ali says that he is certain about Alice not knowing about the bus timings as well. This implies that -
1. The minute cannot be a unique number, like in 0643 & 0746
2. Taking the above point into consideration, we rule out all 0600 and 0700 timings. If Alice had been given one such unique minute, then it would have been easy for Ali to choose between 0643 or 0746 hours.
Now, we are left with the timings for 0800 and 0900 hour buses.
0819, 0832, 0917, 0919, 0950
Alice exclaims, "I didn't know his bus, but now I do!"
Considering the fact that Alice is sure about the exact minute, we can eliminate 0819 & 0919. Or else, Alice would still would have been in confusion. Hence, we have the following timings -
0832, 0917, 0950
As we can see from the lot, the only unique timing here is 0832. This is why Ali responds, "Now I do as well!"
Ans) Anil's bus leaves at 0832 hrs
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