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Diamonds

This area contains buried diamonds. In some places, a number is given: this indicates how many neighbouring (horizontally, vertically or diagonally) cells contain a diamond. A cell with a number never contains a diamond. The number next to the diagram indicates how many diamonds are in the field in total.

Example

In this example, five diamonds have to be placed. To start, we note that the diagram contains a 3 and a 4, which together need seven diamonds. Since there are only five available, there must be at least two diamonds that are adjacent to both the 3 and the 4. There are only two such cells, so they must both contain a diamond. After this, we see that the 1 in the bottom row already has a neighbouring diamond, so all its other neighbours must remain empty.

The other 1 now has only one remaining location for its diamond, so we can place it there. Also, the 2 in the bottom right has only one remaining location for its second diamond. We now placed four of the five diamonds. The 4 and the upper 2 both still need one more diamond, so we place the last one in the remaining cell that is adjacent to both.

Background

This puzzle has many similarities to Microsoft's famous one-person computer game "mine sweeper". The difference is that in the game, you can get into positions where you have to guess (in fact, you start in one), and your information grows during the game, while with diamonds puzzles, all information is given in advance, and is sufficient to find the unique solution.


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