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Shadows

It is a hot and sunny summer's day. Of course customers will only come to the terrace if all tables are in the shadow.

The locations of the tables are already given. You need to place the sunshades on some of the indicated positions, such that all tables recieve some shadow. A sunshade gives shadow to its four adjacent squares. The number next to and under the diagram indicate the number of sunshades that must be placed in each row or column.

Example

In this example we need to place four sunshades: one in each row and column. These sunshades need to protect five tables. We can see that three of them are standing apart, so no sunshade can protect more than one table including one of these. This means that the fourth sunshade must protect both remaining tables: the two in the middle.

Let's turn our attention to the table to the far left. This table could be shaded by two possible locations. However, the bottom one is no longer possible, since there is already a sunshade in the same row. This means we need to use the top one.

This new sunshade now allows us to use the same reasoning with the remaining two tables. The bottom table cannot be shaded from the left, so it must be shaded from the right. The rightmost table cannot be shaded from below, so the last sunshade must placed be in the top right corner.

Background

This genre was invented by Hns Eendebak, head editor of the puzzle magazine Breinbrekers and captain of the Dutch puzzle team.


Puzzles in this genre.
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