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Visual representation of puzzle arrangements with varying dimensions and colorful tile patterns.

A series of four rectangular grids, each filled with colorful puzzle-like shapes, labeled with dimensions: 6×10, 5×12, 4×15, and 3×20.

A series of four rectangular grids, each filled with colorful puzzle-like shapes, labeled with dimensions: 6×10, 5×12, 4×15, and 3×20.

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Show Answer Key & Explanations Step-by-step solution for: pentomino puzzle | Math patterns, Graph paper art, Math games
- The task is to identify the pattern or rule governing the arrangement of Tetris-like pieces across the four rows.
- Each row contains a set of distinct, colorful geometric shapes (tetrominoes) arranged horizontally.
- The goal is to determine what changes from one row to the next and predict the next state or explain the transformation.

Step 1: Analyze the first row.
- The first row has 4 pieces: pink L-shape, purple T-shape, green S-shape, blue I-shape.
- They are arranged in a compact, interlocking manner.

Step 2: Compare with the second row.
- The second row also has 4 pieces, but their positions and orientations have changed.
- The pink L-shape is now at the bottom left, the purple T-shape is in the middle, the green S-shape is on the right, and the blue I-shape is at the top right.
- The arrangement is less compact, with more spacing.

Step 3: Examine the third row.
- The third row shows further rearrangement.
- The purple T-shape is now on the far left, the green S-shape is in the middle, the pink L-shape is on the right, and the blue I-shape is at the far right.
- The pieces are more spread out.

Step 4: Look at the fourth row.
- The fourth row has the same 4 pieces, but they are now arranged in a linear, side-by-side fashion with no overlapping.
- The order from left to right is: purple T-shape, green S-shape, pink L-shape, blue I-shape.

Step 5: Identify the pattern.
- The pattern appears to be a progressive "unfolding" or "separation" of the pieces.
- Row 1: Pieces are tightly packed and interlocked.
- Row 2: Pieces are slightly separated but still somewhat connected.
- Row 3: Pieces are more spread out, with minimal contact.
- Row 4: Pieces are completely separated and aligned in a straight line.

Step 6: Determine the rule.
- The rule seems to be that with each subsequent row, the pieces are moved apart from each other, reducing overlap and increasing spacing.
- The final row shows the pieces in a fully separated, linear arrangement.

Step 7: Verify the pattern.
- The transformation from row to row is consistent: decreasing overlap and increasing separation.
- The order of the pieces in the final row is not random; it follows a specific sequence (T, S, L, I).

Conclusion:
The solution is that the image demonstrates a progressive separation of tetrominoes from a compact, interlocked arrangement to a fully separated, linear arrangement. The rule is the systematic increase in spacing between the pieces across the rows.
Parent Tip: Review the logic above to help your child master the concept of pentomino puzzle worksheet.
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