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Penta

Put the given pieces in the diagram. The pieces can be rotated and/or reflected, but never touch, not even diagonally. The numbers next to and below the puzzle indicate how many squares in those rows and columns are occupied. Some puzzles have completely black squares in them, those are not part of any of the pieces, but they are allowed to touch them. The given pieces are all tetrominoes or all pentominoes, i.e. all shapes you can make with four or five squares.

Example

In the example puzzle five different tetrominoes have to be filled in. These shapes you might know from the computer game Tetris.

For starters we can identify a few spots that are not part of any of the tetrominos for sure: In four locations there is both a 1 below the column and a 1 next to the row. Suppose such a square would be taken, then it would not be connected with anythingelse. Therefore we can mark these squares as unused with the right mouse button.

Of four pieces one square is already known (they are too far apart to be part of the same piece). Somewhere we have to squeeze in a fifth piece without touching the other tetrominoes. That can happen only if the 4x1 tetromino is in a horizontal position at the 4th row. There are two ways to do this, but it can not be to the right, because that would require the entire 3rd row to be empty, so it has to be on the left. Now we see that on row three and five the rightmost square has to be occupied. Both can only be connected to something else in the vertical direction, so we can fill in two more squares in the rightmost column. With this the count of occupied squares in that column reaches the required four, so the remaining two squares have to remain empty.

On the bottom row four squares have to become occupied. If less than three would be to the left of the middle, at least two should be to the right of the middle and those would contribute to a piece of size at least five. That is not the intention, so exactly three of them have to be to the left of the middle. The fourth can not be in the fifth column, because it would touch something diagonally that it can not be part of, so it has to be in the sixth column.

In the meanwhile the first and sixth column meet their requirements. Now we can first finish the piece in the upper right corner and then the piece in the upper left.


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