Problem of the Week 1077


The March 21 New York Times had a nice article by Will Shortz on several new types of puzzles originating in Japan: Inside Japan's Puzzle Palace (requires registration with

I found nurikabe (also known as Islands in the Stream), invented by Nikoli, to be particularly pleasing.

This diagram gives a simple nurikabe, along with its solution:

The idea is to color each square black or white, subject to the following rules, where "connected" always means in a horizontal or vertical direction, not diagonal.

  1. Each numbered square will be white.
  2. Every connected white region contains exactly one of the given numbers, and the number of squares in the region equals the number it contains.
  3. The set of all black squares is connected.
  4. The set of all black squares does not contain a 2×2 set of black squares.

So in this 9×10 nurikabe -- Problem 1077 -- one knows immediately that the three squares connected to the "1" are black.

Source: Wikipedia.

© Copyright 2007 Stan Wagon. Reproduced with permission.

26 March 2007