On the right we see the bottom row after gathering. On the left we press one button at a time. Let's summarize the facts that can be found experimentally: What we need to learn is the effect of pressing the buttons in the first row, on the state of the buttons at the bottom after gathering. Selecting and pressing a few buttons in the first row.Solving the puzzle then can be done in three steps: Then press those buttons in the third row that are beneath the lit buttons in the second. You start in the second row and press the buttons which are just below the lit buttons in the first row. Furthermore, since double clicking a button leaves a configuration unchanged, every 5×5 configuration can be obtained from the bottom 1×5 configuration by clicking exactly same buttons.įor the sake of reference, the procedure that leads to switching off all the buttons in the first four rows is called gathering. In other words, every 5×5 configuration of buttons is reducible to a 1×5 configuration of the last row. The most important observation in this puzzle is that with the given geometry of the neighborhoods it is always possible to reach a state in which all the buttons in the first 4 rows are off. There are notational shortcuts that make the Description manageable, but for the sake of variety I shall present a more intuitive approach. Here we deal with vectors with 25 components and 25×25 matrices. It can be shown that a solution does not always exist and, for this reason, when it does, it is not unique. Like the games of Merlin's Magic Square and Mini Lights Out, this one admits a theory based on linear algebra. |Contact| |Front page| |Contents| |Games| |Eye opener|Ĭopyright © 1996-2018 Alexander Bogomolny For a given configuration, the task is to turn all the buttons off (out.) Pressing a button changes its state and that of its vertical and horizontal neighbors. It consists of a 5×5 array of buttons that may be in one of two positions: on or off. Lights Out is a commercially marketed (by Tiger Electronics) product whose analysis admits a linear algebra framework analogous to that of Merlin's Magic Square puzzle.
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