While it might be an overly complicated puzzle type, Battleship Sudoku holds a special place in my heart as one of my first original creations that also launched my puzzle publishing career with my first book. It was an easy choice to include this type as a hybrid of Battleship Puzzles and Sudoku Puzzles on the Double Decathlon test.
Place the digits 1 through 6 (1 through 9 in the larger grid) into the empty cells in the grid (a single digit per cell) so that each digit appears exactly once in each of the rows, columns, and bold outlined regions. A fleet of ships must also be placed into the grid according to standard Battleship rules: no ships are adjacent (even diagonally) and the number of ship segments in a row/column is given by the digits outside the grid. Ships cannot be placed in any square with a given number, and some unlabelled ship segments or seas may already be given in the grid. Each ship segment in the fleet is numbered, and these numbers will be used to complete the Sudoku solution; the numbers on the ships can be entered in any orientation, allowing for rotation of the large ships.
These two puzzles are greatly assisted by making some observations about the fleet. In the easy puzzle, all six of the ships contain a 1, which means all of the 1's in the grid come from as yet unplaced ships. The two columns that contain only 1 ship segment can only contain a ship segment with a 1. This will get the cruiser placed which should eventually give the rest.
The Hard puzzle shows another theme I really enjoy using as it has some different "meta" thinking. All the ship segments are even, which means only spots that can take even numbers can be ship segments. And when a row/column has 4 ship segments, you must find a way to get all evens placed into ships in a valid way. One sticking point of this puzzle needs you to work through this exact thinking.
After placing the battleship and doing some sudoku solving, you should get to a point like this. The fifth column has a hidden 4, which means all of its even numbers must belong to ships. Without knowing where the 4 and 8 go in that column yet, you must use the available ship inventory to get the correct placements. This leaves just one more spot for the second ship segment in column 4 which will get you to the endgame which involves placing the two cruisers and the remaining ships.
I thought these were pretty good puzzles for this test, but then having written over 200 of them I can pull out a familiar theme in a new way pretty easily, so those with a lot of book solving experience might not have been as intrigued. You can tell me.