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Find Merkle (Posted on 2012-01-18) Difficulty: 3 of 5
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?

No Solution Yet Submitted by brianjn    
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Exploration | Comment 9 of 11 |
The 4 direction game of Merkle was good fun in my classroom some 15-20 years ago.

I doubt that the play would have been less different by employing 8 directions; rather like, " I have a number .....  higher, lower!".

I saw more value in introducing probability as an influence upon the outcome, and so my proposal.

I hoped that my rules were coherently steadfast (other than same_row- same_column noted prior, I'd probably program for one outcome, it would be interesting though to see how allowing 45 offset quadrants played out).

Computer programming!  My disclosure.  Should this surface in some form of APP then I suggest it be reported to levik as breach of "intellectual property", not only being of my proposal, but of the thoughts of those offering solutions.

  Posted by brianjn on 2012-01-19 07:46:48
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