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Shooting them blanks (double optimization task)

Puzzling Asked by Thomas Blue on February 25, 2021

I don’t know the answer, I just state that this problem could be interesting.

Best estimate gets the tick.

"Battleships" game field (at least, in the USSR version I used to play) is a 10×10 grid, that has one ship four cells long, two three cells long, three two cells long, and four one-cellers.

You can place the ships on the board (as long as they don’t touch even by the angles). Then you can shoot into the board, but only miss the ships. The ‘independent audience’ will only see the result of your shots (which are all misses), and not know the ships location (but know the rules). You cannot shoot into one cell twice.

Now, the optimization problems are those:

Sniper

What is the minimum amount of shots required to prove that the ships are located exactly as they are located (i.e., for every cell occupied by ship you can prove conclusively that it really is) ?

Ninja

What is the maximum amount of shots you can make, so that you cannot prove that any given cell is occupied by ship (i.e., for every cell that is not yet shot you can set an example of game field, where it is not occupied)?

5 Answers

The answers are, unfortunately,

Why?

[EDIT: The above is all wrong, because I missed the part about ships being nonadjacent.]

With that settled, I can get a score for Ninja of at least

Answered by AxiomaticSystem on February 25, 2021

Sniper:

Ninja:

Answered by Nautilus on February 25, 2021

For Ninja it's

because

Answered by trolley813 on February 25, 2021

For the sniper question I think here is an answer of only

The shots are:

There is only one way to place the size-4 ship between these shots:

Then only one way to place the size-3 ships:

Then only one way to place the three size-2 ships:

And that leaves only 4 available spots for the small ships.

Answered by Jaap Scherphuis on February 25, 2021

For Ninja, I could get

For example:

This allows the following arrangements of ships:

There is also a near-solution for

For Sniper, I could get a small improvement on the previous best answer posted:

The following pattern of missed shots can work for this total:

Placing the size-4 ship:

Placing the size-3 ships:

Placing the size-2 ships:

Placing the size-1 ships:

Answered by Steve on February 25, 2021

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