Maths Teaser 2

[YOmama]

A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Dick Harvey to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr. Harvey.

[CaptainEd]

I'll go for 9 calls-18 minutes.

Since the OP says they're in alphabetic order, we can do divide and conquer starting in the middle, name number 153.

[Pickett]

Might not be minimum...

But you could deliver the message to Mr. Harvey in AT WORST 50 minutes...or 25 calls.

Start by calling the 25th person on the list....if their name is earlier (alphabetically) than Mr. Harvey, then call the 49th person on the list (24 further)...if if that person is still earlier than Mr. Harvey, call the 72nd person on the list (23 further)...etc...etc...until you get a person that is later (alphabetically) than him. Once you find someone "later", you simply start calling one at a time between the two...

You could actually then do a divide and conquer approach once you have it narrowed down, which in the long term would make the search faster...but for a SINGLE instance like the OP...to GUARANTEE the message is delivered, it doesn't matter if you do one at a time or divide and conquer, it would still be at worst 25 calls.

Edited September 14, 2015 by Pickett

[Pot of Beans]

610 minutes. 

There are 305 different people but that doesn't mean that Dick Harvey can't be the very last one, so to say that probability wise he's around the 51st is only a probability and not a definitive answer which is being asked for, so the call center agent must accept the possibility that Dick could be the very last number on the list because if she were to call every number Dick would have to be one of them, so for a definitive answer she would have to call everyone which would take 610 minutes.

[YOmama]

@CaptainEd Bro U got it.18 is the right answer