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About: Think-a-Dot

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The Think-a-Dot was a mathematical toy invented by Joseph Weisbecker and manufactured 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.

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  • The Think-a-Dot was a mathematical toy invented by Joseph Weisbecker and manufactured 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. (en)
  • Think-a-Dot是公司於1960年代所推出的一款,其用作原理與自動機理論相關。Think-a-Dot的前方有八個窗口,以最上層三個、中間層兩個,最下層三個的方式排列。頂部有三個圓形孔洞,供小球投入。每個窗口都會顯示黃色或藍色的有色塑膠片,這取決於小球由上方孔洞投入後在玩具內部的運作方式。因此,此玩具盤面上的顯示狀態將有28(256)種可能情況。當球落至底部時,會經由底部兩側的開口滾出。當將球投入玩具時,小球將翻轉其通過的窗口顏色,並依翻轉後的顏色決定球偏向左邊或右邊向下一層落下。Think-a-Dot可以實現各種難題和遊戲,例如以最小移動次數翻轉所有窗口的顏色,或者從單色狀態達到指定圖形狀態,反之亦然。 (zh)
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  • Think-a-Dot是公司於1960年代所推出的一款,其用作原理與自動機理論相關。Think-a-Dot的前方有八個窗口,以最上層三個、中間層兩個,最下層三個的方式排列。頂部有三個圓形孔洞,供小球投入。每個窗口都會顯示黃色或藍色的有色塑膠片,這取決於小球由上方孔洞投入後在玩具內部的運作方式。因此,此玩具盤面上的顯示狀態將有28(256)種可能情況。當球落至底部時,會經由底部兩側的開口滾出。當將球投入玩具時,小球將翻轉其通過的窗口顏色,並依翻轉後的顏色決定球偏向左邊或右邊向下一層落下。Think-a-Dot可以實現各種難題和遊戲,例如以最小移動次數翻轉所有窗口的顏色,或者從單色狀態達到指定圖形狀態,反之亦然。 (zh)
  • The Think-a-Dot was a mathematical toy invented by Joseph Weisbecker and manufactured 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. (en)
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  • Think-a-Dot (en)
  • Think-a-Dot (zh)
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