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Ripple

Place the numbers 1 to n exactly once in each region of n cells. For example, in a region with three cells the numbers 1, 2 and 3 must be placed. Between two instances of the same number in a row or column there must be at least that many cells (or a completely black cell). For example, between two fours in the same row there are at least four cells which cannot contain a four, or there must be at least one black cell between these fours.

Example

Start with the central region of only one cell which must contain a 1. Now consider the top right region where a 1 must appear in the top cell as it cannot be adjacent to the other 1. This then provides the 2 in the cell below to complete the region. Similarly, the top-left cell is the only place where a 1 can appear in the top left region in order to not be adjacent to the central 1. The middle row cannot contain another 2 or they would too close, so the final cell must contain a 3, and the remaining cell on the top row must be a 2. For the bottom row, the only possible place for a 2 is the bottom-left cell, and in the middle cell only a 3 can be placed. Hence the bottom-right cell contains the 1.

Background

Ripple is an original puzzle of Nikoli released under the name "Ripple Effect"


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