25 replies to this topic

[sseth]

Mr.X has five boxes arranged in a line (1-2-3-4-5). An intelligent rat comes out of nowhere and finds a place for itself in one of the boxes. Every night when Mr. X is sleeping, this rat moves to a new neighboring box to its left or to its right. Mr. X knew this behavior of the rat. Since this rat was a trouble for him, he was desperate to find it. Also due to paucity of time, he decided to search in only one of the boxes every day. He implements a strategy to make sure that he eventually finds this rat. This strategy helped him to find the rat in minimum number of trials in all cases possible. What is the minimum number of trials needed to come to the solution for all possible cases?

[Swamphawk]

I keep coming up with 5 with almost no strategy. Start on one end and go across.

[thoughtfulfellow]

I keep coming up with 5 with almost no strategy. Start on one end and go across.

This strategy will not work! Remember that the rat can move 1 box left or right.

Spoiler for scenario showing that moving one end to other will not work

rat only moves while you sleep
rat starts in box 4 --> you select 1.
rat moves to box 5 ---> you select 2.
rat moves to box 4 ---> you select 3
rat moves to box 3 ----> you select 4
rat moves to box 2 -----> you select 5
5 sequential guesses and 5 misses.

How intelligent can the rat be if it sets a pattern of predictability of only 1 box shift?

[14.swapnil.14]

Spoiler for Is it

7 trials
Strategy: search order for boxes :- 2 2 3 4 4 3 2

[sseth]

Spoiler for Is it

7 trials
Strategy: search order for boxes :- 2 2 3 4 4 3 2

Hi
Can u please elaborate on this strategy?

[14.swapnil.14]

Hi sseth

Spoiler for Strategy

Suppose rat is under 1
so rat will be caugth in second try.
If rat under 3 initially,
if it moves left after 1 try then it will be caught in second try.
It can also move towards right (under 4)
this situation is similar to another one(if rat was under 5 then it will move to 4)
So after two trys rat at 3 and 5 could be at 5 or 3.
If at three caught after 3rd try.
if at 5 then lift 4 twice so rats initially at 3 or 5 will be caught in 5th try.(only one possible move for end boxes)
Now if the rat is under 4 initially,
possible moves for rat
3 2 3 2 3 so caught in 6 th move
3 2 3 2 1 2 so caught in 7th move.
5 4 3 so caught in 3rd try
5 4 5 4 caught in 5th try

So rat is guaranteed to be caugth in 7 trys.

Spoiler for Update

Chelsea 3- 5 Arsenal

[sseth]

Hi sseth

Spoiler for Strategy

Suppose rat is under 1
so rat will be caugth in second try.
If rat under 3 initially,
if it moves left after 1 try then it will be caught in second try.
It can also move towards right (under 4)
this situation is similar to another one(if rat was under 5 then it will move to 4)
So after two trys rat at 3 and 5 could be at 5 or 3.
If at three caught after 3rd try.
if at 5 then lift 4 twice so rats initially at 3 or 5 will be caught in 5th try.(only one possible move for end boxes)
Now if the rat is under 4 initially,
possible moves for rat
3 2 3 2 3 so caught in 6 th move
3 2 3 2 1 2 so caught in 7th move.
5 4 3 so caught in 3rd try
5 4 5 4 caught in 5th try

So rat is guaranteed to be caugth in 7 trys.

Spoiler for Update

Chelsea 3- 5 Arsenal

Thanks alot!!!!

[Jack Page]

Spoiler for

1, look where there is rat droppings the first morning, and the rat will be in there.

[superguy]

Look which one is moving most. Duh!

[wolfgang]

put rat poison in the boxes..2,3,4,and 5....check only number 1...lol