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The Think-a-Dot was a mathematical toy made by E.S.R., Inc. during the 1960s that demonstrated automata 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.

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  • Schwartz, Benjamin L. (1967), "Mathematical theory of Think-a-Dot", Mathematics Magazine, 40 (4): 187–193, doi:10.2307/2688674, MR 1571696.
  • Beidler, John A. (1973), "Think-a-Dot revisited", Mathematics Magazine, 46: 128–136, doi:10.2307/2687967, MR 0379077.
  • Gemignani, Michael (1979), "Think-a-Dot: a useful generalization", Mathematics Magazine, 52 (2): 110–112, doi:10.2307/2689850, MR 1572295.

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