Question

*Puzzle Alert:*
Steve is taking a bus to the Central Park. Steve tells Alice the hour of his bus departure and he tells Annie at which minute it leaves. He also tells them both that the bus leaves between 0600 and 1000.
Alice & Annie consult the timetable and find the following services between those two time: 0632 0643 0650 0717 0746 0819 0832 0917 0919 0950.
Alice then says "I don’t know when Steve’s bus leaves but I am sure that neither does Annie"
Annie Replies "I didn’t know his bus, but now i do"
Alice responds "Now I do as well!"
When is Steve’s bus?

Answer 1

According to the question, Alice says, "I don’t know when Steve’s bus leaves but neither does Annie”.

We know that she only knows about the hour of departure of the bus (either 0600/0700/0800/0900 hrs). Thus, it is difficult for Alice to tell the time without knowing the exact minute. Moreover, Alice states that she "is sure" about Annie not knowing about it as well. So, it is observed that -

1. The minute cannot be unique digits, like in 0643 and 0746.

2. If Annie had been given a unique digit, like in 43 or 46, then Alice would have easily identified the timing among 0600 or 0700 hours. Hence, we eliminate all 0600 and 0700 timings.

Now, we have the bus timings for 0800 and 0900 hours - 0819, 0832, 0917, 0919, 0950

Annie had said, "I didn't know his bus, but now I do!"

On the basis of Annie's response, we remove 0819 & 0919 from the set. Otherwise, it would have been difficult for Annie to identify the correct bus timing. So, we narrow it down to the following options -

0832, 0917, 0950

Alice's exclamation - "Now I do as well!" - provides us the final point; the unique hour in this lot is the time of departure of Steve's bus. That is, 0832.

Ans) Steve's bus leaves at 0832 hrs

A similar solution is available here -

brainly.in/question/16496302

brainly.in/question/16464719

https://brainly.in/question/16473155

Answer 2

Steve's bus departs at 0832

Explanation:

Alice doesn't know and Annie doesn't know as well. So this let's us to eliminate the unique minutes. That removes 0643 and 0746 off the list.

This let's us to eliminate all time slots of 6 hours and 7 hours as well.

So let's remove 0632, 0650, and 0717.

We are left with five choices: 0819, 0832, 0917, 0919, 0950

Annie later realizes what the bus time is. So it can't be a timing that is not unique. So let's remove repeat minutes 0819 and 0919.

We are left with  0832, 0917, 0950.

Again, we can't have something that is not unique. Only then they could have guessed the answer. We have repetition in 9 hours, but 8 hours timing is only one.

So that's the obvious choice.

Steve's bus departs at 0832.