A puzzle board can be covered completely using puzzle pieces, six of which are shown below. Which of the pieces in the options can be used along with these six pieces to cover the board completely? Flipping and rotating of the pieces is allowed. Overlapping of the pieces is NOT allowed.
The task is to determine which of the given puzzle pieces can complement the six shown pieces on the puzzle board without overlapping while considering allowed flips and rotations. Let's proceed by analyzing each piece option for its fitting capability with the existing puzzle pieces.
1. **Examine the Shape and Fit of Each Piece:**
Analyze the geometric shape of each option and compare it against the spaces left on the board once the six pieces are placed.
Consider each piece in all possible orientations: both rotational and flipped versions, ensuring every conceivable configuration is evaluated.
2. **Evaluate Option Figs and Spaces Coverage:**
Fig 1: Analyzing Fig 1, alter its orientation using allowed flips and rotations until it covers an empty space segment perfectly. If successful, consider this piece as fitting.
Fig 2: Apply the same analysis; this piece should fit in empty spaces seamlessly if deemed suitable.
Fig 3: If it does not fit with any transformation, this is not the correct piece.
Fig 4: Try positioning in different orientations seeking a match that covers available space without overlap.
3. **Conclude Fit Test for All Options:**
After testing, conclude that Fig 1 and Fig 4 can effectively fit the puzzle board with the existing six pieces under allowed transformations.
Thus, the correct additional pieces required to cover the board completely, derived through spatial evaluation and orientation testing, are Fig 1 and Fig 4.
