# Puzzle 50: Sea of Ships

Follow similar Fillmats rules. Divide the grid into several rectangles, each of which must have 1-unit width and a height of between 1 and 4 units inclusive (or vice versa). No two rectangles with equal area may be orthogonally adjacent. A number gives the size of the rectangle it’s contained in. Differences from usual Fillmats rules: You can have multiple numbers in the same rectangle (like Fillomino), and four rectangles may meet at a point.

Afterwards, interpret the rectangles as usual Battleships ships, and solve the resulting Retrograde Battleships puzzle. Mark some of the ships black so the exact quantity of ships as shown in the fleet below are marked (aka for this puzzle, 1 battleship of 4-unit length, 2 cruisers of 3-unit length, 3 destroyers of 2-unit length, and 4 battleships of 1-unit length). No two ships may touch each other even orthogonally. Numbers outside the grid gives the number of ship segments in the corresponding row/column.

“Have you identified the ships Sky?”
“What? Are you expecting me to do this task really quickly? I even have no prior experience.”
“Just try.”
“Yeah, I’m trying if you can’t tell. Or actually…I think we can deduce all the ships from only this information.”
“Are you serious?”
“Hopefully so. Just try; if you miss something, I’ll try to identify something that will help. But see, this is more efficient with not that much cost to identify everything…”
“Yeah yeah I know, Sky the Puzzle Master. Okay, let me solve this.”
“Also, seeing from the information, if it’s unique then it should be medium, but let’s see…”

Puzzle 50: Sea of Ships