There are 5 boxes arranged in a row. A robot is hiding in one of those boxes.Each day the robot secretly jumps to one of the adjacent boxes.Each day you can open a box.Give a sequence for opening the boxes each day so that the position of the robot is finally found out.You can take any number of days.
Answer through comments
OPEN THE BOX IN THE MIDDLE....
ReplyDeletewhat if the robot jumps within the first 2 boxes?
ReplyDeleteSo opening the middle box won't make it sure that position of the robot is determined
but your question states that it jumps to the adjacent box("A robot is hiding in one of those boxes.Each day the robot secretly jumps to one of the adjacent boxes"), so the robot has to obviously pass through the middle box.
ReplyDeleteNot necessarily it says it jumps to the adjacent box.
ReplyDeleteWhen the bot is in box 1 , box 2 is the adjacent box.
And when the bot jumps to box 2 , it can either go to box 1 or the middle box.
So there is a case when it just jumps between box 1 and box 2
ReplyDeletesequence 2, 2, 3, 4, 4, 3, 2 will guarantee that we find the robot at some point during the sequence
first 2, 2 will take care of I= {1,2} cases
next 3, 4 will take care of I={3,5} cases.
only case left is I={4} case.
Since all the other initial cases are taken care of by now, we are free to extend the monitoring sequence from now on as we wish just to take care of I={4} case.
Now only position the robot could be in are {1,3}.
Now the robot is to the left of us. To make sure he stays left of us, we monitor 4 again.
From now on it is easy to follow solution.
First of all congrats...
ReplyDeleteSecondly, You could fix the position of the bot in only 4 openings.
Clue:Your answer already contain that sequence.
Btw You could post your name if you wish to publish (winner: )
The shortest solution will be published on 5 feb
The shortest answer is 2 3 4 4.
ReplyDeleteWhen you open 2 the bot can be in 1 3 4 5.
When you open 3 the bot can be in either 2 4 5 (if it was in 1 earlier it would jump to 2)
Now open 4 , its either in 1 3 5 but not in 2.
Open 4 again, the bot if in 1 or 3 would jump to 2,if in 5 it would be caught jumping to 4.
Now we know the bot is in 2 for sure