Think-a-Dot
Encyclopedia
The Think-a-Dot was a mathematical toy made by E.S.R., Inc. during the 1960s that demonstrated group theory
. It had eight coloured disks on its front, and three holes on its top - left, right, and center - through which a ball bearing could be dropped. Each disk would display either a yellow or blue face, depending on whether the mechanism behind it was tipped to the right or the left. The Think-a-Dot thus had 28=256 internal states. When the ball fell to the bottom it would exit either to a hole on the left or the right of the device.
As the ball passed through the Think-a-Dot, it would flip the disk mechanisms that it passed, and they in turn would determine whether the ball would be deflected to the left or to the right. Various puzzles and games were possible with the Think-a-Dot, such as flipping the colours of all cells in the minimum number of moves, or reaching a given state from a monochrome state or vice-versa.
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
. It had eight coloured disks on its front, and three holes on its top - left, right, and center - through which a ball bearing could be dropped. Each disk would display either a yellow or blue face, depending on whether the mechanism behind it was tipped to the right or the left. The Think-a-Dot thus had 28=256 internal states. When the ball fell to the bottom it would exit either to a hole on the left or the right of the device.
As the ball passed through the Think-a-Dot, it would flip the disk mechanisms that it passed, and they in turn would determine whether the ball would be deflected to the left or to the right. Various puzzles and games were possible with the Think-a-Dot, such as flipping the colours of all cells in the minimum number of moves, or reaching a given state from a monochrome state or vice-versa.