Passengers in the Ships!

Logic Level 4

There are twelve ships situated on a \(10 \times 10 \) grid. The ships are denoted by the letters \(A\) through \(L\), and each ship consists of three cells of the grid in either a horizontal or a vertical line, as shown in the diagram. Each ship contains a certain number of passengers. There are also some numbers in the last row and the last column of the diagram. These numbers represent the total number of passengers on all the ships intersected by that row or column.

For example: The two ships \(B\) and \(L\) intersect the right-most column, so together they contain 9 passengers. The two ships \(G\) and \(L\) intersect the bottom-most row, so together they contain \(6\) passengers.

Given that there are no passengers on two of the ships and the remaining ten ships contain \(1,2,3,4,5,6,7,8,9\) and \(10\) passengers, let the number of passengers each of the twelve ships \(A\) to \(L\) contain be represented by their respective denoted letters. Then find the value of:

\[\large{AB + C + \dfrac{D}{E} + F^G + \dfrac{H}{I} + J - K + L^L = \ ?} \]


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