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Suppose I have a standard Battleship Puzzle, but with no clues (no square uncovered) at the start. Then I'm given 5 "fires" that uncover a square, what would be the best strategy to chose a square to uncover?

Puzzle example

Edit:

In the first picture I have the board, the second one is the starting position which unique solution is the board from pic1 and the final picture is my initial state, from which I, ideally, want to obtain a state which unique solution produces the board from pic1

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    $\begingroup$ Isn't this essentially asking what the best strategy is for the two-player game of Battleship? $\endgroup$ – Jaap Scherphuis Jun 11 at 16:38
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    $\begingroup$ Then how do we answer the question? It will depend on the outside numbers. Some grids are fully solvable no matter which five cells you choose, because they're solvable without any internal clues at all. $\endgroup$ – Deusovi Jun 11 at 16:45
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    $\begingroup$ What's the metric? Highest chance of hitting any ship? Minimizing the length of smallest ship hit (the smallest are hardest to find) ? What's the opponent model, random placement, adversarial placement? $\endgroup$ – Jeffrey Jun 11 at 18:16
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    $\begingroup$ @Jeffrey, yes, those should be used, it's the point of the battleship puzzle $\endgroup$ – Sepfins Jun 11 at 19:01
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    $\begingroup$ Is the intended result here just getting a single hit? $\endgroup$ – Ian MacDonald Jun 11 at 19:23
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So, here's what I might do:

I would probably start where the largest numbers intersect as I would probably have the best chance to hit something there. For example, the 5 and 4.

If so, the rules state I would then know the shape of what was underneath. Thus, knowing the direction the ship was facing (if an end piece) or if the ship was larger than one cell (middle section).

As I progressed, I would follow the direction of the hit ship and try to stay away from any 0,0 or low-number intersections since I only have 5 attempts and they would be wasted.

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The best strategy is to

try top-left, top-right, bottom-left, bottom-right.

I play with my son and he always try to hide a ship there.

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    $\begingroup$ unappreciated humour :-) $\endgroup$ – Jeffrey Jun 11 at 18:49

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