Friday puzzle -- Nurikabe

Can't see the picture

No picture at 11:00.  What is goal?

Let's try that again

Alex Y

Sorry about that. I had drafted the note last night, but didn't send until this morning, and during that time, the system lost the pic, but still showed that a pic was attached. Weird!

Below is a Nurikabe puzzle. If you are familiar with them, skip the instructions--they are standard unless I mess it up.

There are 100 square, each of which is to receive either a black or white tile, which you must determine. There are three conditions that your solution must meet:

* The black tiles are all connected in one continuous region (two tiles are connected if they share an edge, not just a corner).

* No four black tiles share a corner. Said another way, any 2x2 set of tiles must include at least one white tile.

* The numbers shown are the number of white tiles in the connected white region containing that number.

Hints

Alex Y

To get you started. Read only as many as you want.

Any square sharing an edge with one of the two "1" squares must be black, since they are in a white region only ones square in size -- seven black squares.

Any square sharing an edge with two different numbered squares must be black, since otherwise, those two numbered squares would be in the same white region -- three more black squares.

One of the black squares you filled in in the first hint can be connected with other black squares in only one way -- one more black square, which also forces two more white squares.

Don't forget those squares far away from the numbered squares. Enough white regions must reach those areas to avoid four black squares in a 2x2 square. For example, look at the squares (8,8), (8,9), (9,8), and (9,9). There are only two white regions that can reach that 2x2 square. and if one of them is used, then then shifting over one to the right or one down will show a 2x2 area that must be all black, so you can identify which region gets into this square, as well as marking out much of that region.

Question

Larry Barrett

Is it the case that the total number of white cells is the sum of the numbers, ie 41?

Re: Hints

Larry Barrett

Assuming the answer to question is yes, my solution has following property:

Row # of white cells per row

1.....4

2.....4

3.....5

4.....5

5.....4

6.....2

7.....6

8.....2

9.....8

10...1

Re: Question

Alex Y

Yes each white region has a number indicating the number of white tiles in the region; i.e., there are no unlabeled white regions.

Alex Y

The correct answer has the same counts, so I would be VERY surprised if your answer were wrong.

Answer

Alex Y

Good job, Larry. Here is the solution he described: