Howdy Fellas! “If the little grey cells are not exercised, they grow the rust.” -Agatha Christie

### Brainbusters

With a halt in the normal routine has come endless free time and with that, sheer boredom which has engulfed all of us by now and dulled our brains.
So MnP brings to you #BrainBusters to stimulate your brain cells. We will post baffling brain teasers to challenge your mind periodically.
Figure out how to solve these and mail us your solution to mnpclub.iitb@gmail.com
Cheers!

### Find Smith

There is a corridor with 20 rooms and Smith is hiding in one of them. Each day, Smith moves to an adjacent room. John can open only one door in a day. John has to find Smith as soon as possible. What is the minimum number of days that John require to guarantee that he catches Smith?

### Who ate my cookies?

Steve, Tony, and Bruce have a plate of 1,000 cookies to share. They decide to share them in the following way: beginning with Steve, each of them in turn takes as many cookies as he likes (they must take an integer amount, greater than or equal to 1), and then passes the plate clockwise (with Tony sitting to Steve’s left, and Bruce sitting to Tony’s left). Nobody wants to feel like he hogged too many cookies, so they all want to avoid being the player at the end who has taken the most cookies. Additionally, nobody wants to feel cheated by finishing with the fewest cookies. Finally, given that the previous two conditions are definitely met, or definitely cannot be met, each player would like to maximize the number of cookies he eats. The players’ objectives can be summarized as follows:
Objectives:
A) Have one player who has eaten more cookies than you, and one player who has eaten fewer cookies than you.
B) Eat as many cookies as possible.
Objective 1 takes infinite priority over Objective 2.

Assuming that all players are perfectly rational, that they are all aware of each other’s rationality and objectives, and that they cannot communicate with each other in any way, how many cookies should Steve take to ensure he meets both objectives and how many cookies will Tony and Bruce take if Steve takes the winning amount?