Few days ago, the notorious Blackbeard sunk 3 of my ships carrying exotic goods and treasures from Asia. I was furious and I am determined to send out my fleet to bring him to justice. However, as he is a well known and a formidable pirate, I need to plan my attack carefully. So I send out a number of scouts, hoping they would be able to locate where they are.
To my delight, my scouts are successful in their first attempt to locate the pirates, and I have received the following message:
There are 10 ships in total, namely 1 flagship, 2 frigates, 3 corvettes, and 4 patrol boats located in the Caribbean sea. It seems like that they are anchored here and won't be moving any time soon. Furthermore, none of Blackbeard's ships touch each other, not even diagonally.
However, my military adviser says we need more information on their fleet formation so he can devise a plan to strike him down from where he is the weakest. So I replied to the scout to bring back that information.
That's exactly what they did, but this time, the information is not complete. The message is as follows
Please see the attached map for the pirate's fleet formation. The numbers are the number of ship pieces on that row or column
The map attached look like this
$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|l} \hline&&&&&&&&&&1\\ \hline&&\blacktriangle&&&&&&&&1\\ \hline&&&&&&&&&&3\\ \hline&&&&&&&&&&1\\ \hline&\blacklozenge&&&&&&&&&4\\ \hline&&&&&&&&&&0\\ \hline&&&&&&&&&&0\\ \hline&&&&&\blacktriangleright&&&&&8\\ \hline&&&&&&&&&&1\\ \hline&&&&&&&&&&1\\ \hline2&1&3&1&1&1&3&1&5&2 \end{array} \quad\quad \bbox[4pt,border: 1px solid black]{ \begin{array}{llc} \bf{Legend:}&\\ \hline \text{Flagship:}& \blacktriangleleft\blacksquare\blacksquare\blacktriangleright \text{or} &\blacktriangle\\ &&\blacksquare\\ &&\blacksquare\\ &&\blacktriangledown\\ \hline \text{Frigate:}& \blacktriangleleft\blacksquare\blacktriangleright \text{or} &\blacktriangle\\ &&\blacksquare\\ &&\blacktriangledown\\ \hline \text{Corvette:}& \blacktriangleleft\blacktriangleright \text{or} &\blacktriangle\\ &&\blacktriangledown\\ \hline \text{Patrol Boat:}& \blacklozenge\\ \end{array}} $$
Clearly, something happened to the scout, and he wasn't able to finish the map. However, after seeing the map, my military adviser smirked and locked himself in the operation room to discuss the tactic with my admiral.
Did he really manage to locate the enemy ships based on that map? Can you deduce all the ships' locations via this map?
Answer
$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|l} \hline&&&&&&&&\blacklozenge&&1\\ \hline&&\blacktriangle&&&&&&&&1\\ \hline&&\blacktriangledown&&&&\blacktriangle&&\blacklozenge&&3\\ \hline&&&&&&\blacksquare&&&&1\\ \hline&\blacklozenge&&&&&\blacktriangledown&&\blacktriangleleft&\blacktriangleright&4\\ \hline&&&&&&&&&&0\\ \hline&&&&&&&&&&0\\ \hline\blacktriangle&&\blacktriangleleft&\blacksquare&\blacksquare&\blacktriangleright&&\blacktriangleleft&\blacksquare&\blacktriangleright&8\\ \hline\blacktriangledown&&&&&&&&&&1\\ \hline&&&&&&&&\blacklozenge&&1\\ \hline2&1&3&1&1&1&3&1&5&2 \end{array} $$
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