Light Up

Light Up (Japanese:美術館 "bijutsukan") is a binary-determination logic puzzle published by Nikoli. As of 2006, two books consisting entirely of "Light Up" puzzles have been published by Nikoli.

Rules

"Light Up" is played on a rectangular grid of white and black cells. The player places light bulbs in white cells such that no two bulbs shine on each other, until the entire grid is lit up. A bulb sends rays of light horizontally and vertically, illuminating its entire row and column unless its light is blocked by a black cell. A black cell may have a number on it from 0 to 4, indicating how many bulbs must be placed adjacent to its four sides; for example, a cell with a 4 must have four bulbs around it, one on each side, and a cell with a 0 cannot have a bulb next to any of its sides. An unnumbered black cell may have any number of light bulbs adjacent to it, or none. Bulbs placed diagonally adjacent to a numbered cell do not contribute to the bulb count.

olution methods

A typical starting point in the solution of a "Light Up" puzzle is to find a black cell with a 4, or a cell with a smaller number that is blocked on one or more sides (for example, a 3 against a wall or a 2 in a corner) and therefore has only one configuration of surrounding bulbs. After this step, other numbered cells may be illuminated on one or more sides, narrowing down the possible bulb configurations around them, and in some cases making only one configuration possible.

When it is unclear where to place a bulb, one may also place dots in white cells that cannot have bulbs, such as around a 0 or in places where a bulb would create a contradiction. For example, a light bulb placed diagonally adjacent to a 3 will block two of its surrounding cells, making it impossible to have three bulbs around it; therefore, the diagonal cells around a 3 can never have lights in them and can be always dotted. Similarly, one may put dots in places where a bulb would "trap" another unlit cell, making it impossible to light it up without breaking the rules.

A more advanced technique is to look for a cell that is not yet lit, and determine if there is only one possible cell in which a bulb can be placed to light it up.

Also, say "1" is diagnal from "2". The two is pushed against a wall of some sort. One bulb can definitely go on the opposite side of the 1, since the other two spots cannot both contain bulbs (Then there'd be 2 next to 1).

ee also

*List of Nikoli puzzle types
*

External links

* [http://www.nikoli.co.jp/en/puzzles/light_up/ Nikoli's English page on "Light Up"]
* [http://www.cs.umass.edu/~mcphailb/papers/2005lightup.pdf Light Up is NP-Complete] (PDF viewer required)