MindMine #3
In the grid below, the number in each cell represents the number of neighboring cells which are shaded, including the diagonals but not including the cell itself: How many of the cells are shaded?
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To make the solution simpler, we can identify the box with letter. Top left box is box A. To the right, consecutively, are box B, C, D. Below box A is box E. To the right, are box F, G, and H. And so on, that bottom right box is box P.
According to box B, there are at most two shaded boxes among E, F, G. According to box N, there are at most 1 shaded box among I, K, M, O However, according to box J, there are exactly 4 shaded boxes among E, F, G, I, K, M, N, O. The conclusion is that: Box N is shaded There are exactly two shaded boxes among E, F, G There is exactly 1 shades box among I, K, M, O
According to box A, there is at most 1 shaded box among E, F. While according to previous conclusion, there are exactly two shaded boxes among E, F, G. That means G is shaded. And there is exactly 1 shaded box among E, F. Also, because around A there is only 1 shaded box, box B is definitely not shaded.
According to M, there is only 1 shaded box around it. Since N is shaded, I and J are not shaded.
According to B, there are two shaded box around it. Since G is shaded and there is exactly 1 shaded box among E and F, Box A is definitely unshaded.
There is one shaded box around E. Now that many around it are found to be unshaded, F is definitely shaded. Since there is only 1 shaded box around box E, box I is unshaded.
There are two shaded box around box I. We already know box F and N are shaded. So box E and M are definitely unshaded.
Around box K, there are three shaded box. Since F, G, and N are already shaded, O is unshaded.
Around box J, there are already 4 unshaded box (E, I, M, O). That means the remaining boxes around it are shaded.
Now, the shaded box already managed to satisfy the numbers in all boxes.