It has been two weeks since I left home. India trip, a week of business meetings and I am finally on my flight back home… It has been a long time since I posted a puzzle on my flight back home on a Thursday evening… so here goes the next one…

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A hotel wing has 17 consecutive rooms numbered 1 thru 17. Each of the rooms are connected to the two adjoining room(s) thru keyed (internal) doors and to the corridor with one (external) keyed door. Of course the two end rooms have only one internal door. A fugitive is holed up in one of the rooms. He has one of the two master keys that can open up the (internal) doors to the adjoining room(s). However, for security purpose, the key, once operated, is inactive for 24 hours. And the key has to be used once every 24 hours – else it gets completely deactivated. In other words, the fugitive has to shift to the next room every day using the internal door – on any one side, unless he is in room 1 or 17, in which case he has only one choice.

There is a detective who suspects that the fugitive is holed up there. He has the other master key. This key also works in the same way except it works only on the external door of the rooms (that opens to the corridor). Thus, the detective can open the external door of any room. If he finds the fugitive there, he apprehends him. If not, he has to immediately shut the door and stay in the corridor (so that the fugitive cannot escape thru the corridor). The detective, can choose to open the same room on consecutive days, if he so desires.

So day after day, this is what happens – the detective opens a room, checks for the fugitive and closes the door if he does not find him. The fugitive, meanwhile, day after day shifts to the room on the left or the right – once a day (as mentioned, unless he is in one of the end rooms, in which case, he can go in only one way).

Now, the detective’s assignment runs out in 30 days. So, he has to apprehend the fugitive within that time period or else he is recalled and the fugitive escapes.

Can you come up with a strategy for the detective (what logic will he follow to open doors) that will guarantee that he will catch the fugitive before he is recalled?