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Enlightenment

A number of lamps have to be placed in the diagram. Depending on the strength, a lamp illuminates a square region of 1, 2, or 3 cells around the lamp. In the diagram, some numbers are given: a cell with a number is illuminated by exactly that number of lamps. Cells with numbers do not contain lamps themselves, and lamps do not touch each other, not even diagonally.

There are three different types of lamps. Candles have a strength of 1, which means that they illuminate all (horizontally, vertically or diagonally) adjacent cells. Lanterns have a strength of 2, which means they illuminate all cells that are at most 2 steps away (horizontally, vertically or diagonally) from the lantern. Finally, light bulbs have a strength of 3, which means that they illuminate all cells that are at most 3 steps away from the lamp.

Example

In this example we need to place 2 candles and 1 lantern. Since a candle can only illuminate 1 step far, no candle can illuminate both given 2s. This means that the lantern has to illuminate both 2s, and that each 2 has to be further illuminated by one of the candles.

Since the lantern has to illuminate both 2s, there are six remaining locations for it. No matter which of those locations is used, it will always also illuminate both 1s. Since the 1s can only be illuminated once, there cannot be any candles adjacent to a 1. The means that the candle that has to illuminate the 2 in the lower left has only one remaining possible location.

The lamps cannot touch each other, so the lantern now has to be in the third column. If it would be directly below the 2, then there would not be any remaining place for the last candle. Therefore it has to be one cell lower, directly above the 1. Now the second candle can only be in the top right corner.

Background

This genre was invented by Bram de Laat, and originally appeared under the name "Gloeilampen" ("Light Bulbs").


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