Question

Steve is taking a bus to 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

Let us look at what Alice says -

“I don’t know when Steve’s bus leaves but neither does Annie”.

Since she has only been informed about the hour at which the bus leaves (i.e. 0600/0700/0800/0900 hrs), it is indeed not easy for her to ascertain the time without knowing the number. Also, she says she "is sure" that Annie does not know about the bus timings too. This implies that -

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

2. Considering the above fact, we eliminate all 0600 and 0700 timings. This is because, if Annie had been given a unique minute like 43/46, then it would have been easy for Alice to choose between 0600 or 0700 hours.

This narrows down our options to the 0800 and 0900 hour buses.

Now, let's look at what Annie says -

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

Let's find how Annie cracked the solution. We are left with the following timings-

0819, 0832, 0917, 0919, 0950

Considering the fact that Annie is sure about the exact minute, we remove 0819 & 0919 from the lot (otherwise, Annie would still have been in a state of confusion). Therefore, we have -

0832, 0917, 0950

This leaves us with one inference via Alice's response,

"Now I do as well!"

This is because, the only unique timing in the lot is 0832, as the other two belong in the 0900 time period.

Ans) Steve's bus leaves at 0832 hrs

A similar solution is available here - https://brainly.in/question/16496302