How Well Do You Know Polyomino?

There are 18 one-sided pentominoes, which are shapes made up of 5 squares connected edge-to-edge. A mirrored pair is a pair of pentominoes that are mirror images of each other. To determine the number of mirrored pairs, we need to find how many pentominoes have a mirror image among the remaining 17 pentominoes. Since each pentomino has a unique shape, there are no duplicates, and therefore each pentomino has a unique mirror image. Thus, there are 18 mirrored pairs in 18 one-sided pentominoes.

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The use of polyominoes in puzzles started in 1907.

Solomon Golomb is credited with inventing the term "polyomino" in 1953. A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. Golomb's work on polyominoes laid the foundation for the field of recreational mathematics and has had applications in various areas, such as computer science and tiling problems. His contributions to the study of polyominoes and his invention of the term have had a lasting impact on mathematics and related fields.

A typical polyiamond is made up of equilateral triangles. Polyiamonds are a type of polyform, which are geometric shapes made by joining together identical smaller shapes. In the case of polyiamonds, these smaller shapes are equilateral triangles. Polyiamonds can be used to create interesting patterns and tessellations, and they are commonly used in recreational mathematics and puzzles.

Polyominoes are shapes made by connecting squares together. They are used to model various systems in statistical physics, such as the behavior of polymers and the arrangement of particles in a lattice. By studying polyominoes, scientists can gain insights into the properties and dynamics of these systems, which can have applications in fields like materials science and condensed matter physics. Therefore, polyominoes are best applied in the science of statistical physics.

Equivalent polyominoes is not a class of polyominoes because it refers to a property or concept rather than a distinct category of polyominoes. Equivalent polyominoes are polyominoes that can be transformed into each other through rotations, reflections, or translations. The other options, fixed polyominoes, one-sided polyominoes, and free polyominoes, are all recognized classes of polyominoes based on different criteria or restrictions.

Mirroring is not associated with polyominoes because polyominoes are made up of connected squares, and mirroring would change the orientation of the squares, resulting in a different shape. Rotation, glide reflection, and translation are all rigid transformations that can be applied to polyominoes without changing their overall shape.

Sudoku is the correct answer because it is a puzzle game that uses polyominoes. Polyominoes are geometric shapes made up of squares that are used to fill a grid in Sudoku. In Sudoku, players must fill a 9x9 grid with numbers so that each column, each row, and each of the nine 3x3 sub-grids contains all of the digits from 1 to 9 without repetition. Polyominoes are used to represent the numbers in the grid, making Sudoku a game that utilizes polyominoes.