An "x-y" grid game that I know as "Find Merkle" [M] requires a player [H] to begin at (0,0) and zero in on a hidden co-ordinate location of the creature by nominating one of the 4 cardinal directions and an integer distance. Upon failure to land on that location you are given just one cardinal direction towards that site.
Supposing "Merkle" is hiding at (5,5) and you are at (3,8) after your second play, which was either E3 or N8, you are told E or S, nothing more.

Let us allow two changes to this.
Firstly the player is told to move in one of 8-point compass rose directions.
Secondly, upon failure to capture, "Merkle", having no knowledge of the hunter's location, randomly relocates to any of his immediately adjacent 8 locations except for one if already occupied by the hunter.
- This is exemplified if "H" has been told "SE" and has relocated to (6,5).

Oh, and the hunter only knows "Merkle's" location upon capture. Given that the hunter is astute and multiple games are played, what is the most likely number of moves to capture "Merkle" within an NxN grid?

(In reply to Many questions by Steve Herman)

Understanding 9) With one of the two changes, the distance the Hunter moves is not necessarily an integer, but a multiple of the square-root of 2.

A question akin to Steve Herman's understanding (6), if the exact direction is not one of the 8 cardinal directions of a compass rose, will the cardinal direction that most reflects the location of Merkle be the one that Merkle must inform the Hunter? If the Hunter is at (0,0) and Merkle is at (1,2) Merkle is NNE of the Hunter, will Merkle tell the Hunter "North", "Northeast", or can he even alternately say "East"?

[A correction to the inital example of the Hunter's second move - the play should be given as E3 or N8].

Posted by Dej Mar on 2012-01-18 22:56:19