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Naoki's Island

A set of islands in the middle of the Pacific Ocean is extremely prone to flooding. Reconstruct the floating platforms so as to link all of them together.

Shade some cells so that all shaded cells and islands are orthogonally connected. Numbers on islands give the number of shaded cells that can be reached from each island before running into another island cell.

Example

First consider the 1. In order for it to reach the rest of the islands, there must be some platforms heading toward the only number within reach (the 3). We now note that the bottom left 3 can only reach the 2, and it can only use one platform in this connection or the 2 has nothing left to reach the rest of the islands. This spare platform from the 2 must bridge the gap to the 4. Now note that there is only one route of two cells connecting the top 3 to the 4, and the remaining platforms from the 4 and left 3 are now forced.

Background

This puzzle was created by Naoki Inaba.


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