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A pentomino is a geometric shape formed by joining five squares edge-to-edge. There are 12 unique pentominoes, which include various configurations like straight lines and L-shapes. If you want to place one pentomino in each row of a grid, the total number of arrangements depends on the number of rows and the specific constraints of the grid. Assuming a standard scenario with no additional restrictions, you could use each of the 12 pentominoes in one row, leading to multiple combinations based on the arrangement rules.

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1mo ago

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How many pentomines with 1 square in each row be built?

There are 12 possible pentominoes, but only 1 has "one square in each row".


How many 3d pentominoes are there in total?

There are 29 distinct pentominoes in three dimensions. 5 pairs of them are mirror images and can be rotated in 4-space to be considered the same. There is one 4D pentomino that cannot be built in 3D for a total of 24 4D pentominoes.


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The four rules for drawing pentominoes are: Each pentomino must consist of exactly five connected squares, with each square sharing at least one side with another square. The orientation of the pentomino can vary, allowing for rotations and reflections, but the basic shape must remain consistent. No two pentominoes can be identical; rotations or reflections of the same shape count as the same pentomino. The pentominoes should be drawn clearly to distinguish each shape, ensuring that they are easily recognizable and defined.


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