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Fission

Cut the shape into a given number of smaller regions of the same shape and size. Cuts have to be horizontal, vertical or diagonal between adjacent dots. The shapes may be rotated, but not reflected. Of course, reflections that are also rotations are allowed. Next to the diagram it is stated how many regions of which size are required.

Example

In the example puzzle on the left, we have to cut the shape into two smaller regions of area six each. We can quickly determine that the two squares sticking out on the right, should not be connected to each other, because you would already need to use six area units and what remains has a different shape. Neither of these squares can have a diagonal cut, because it would separate a small triangle from the rest of the shape.

These two squares can not fulfill the same role within their respective regions, because in that case the entire third row would not be able to be part of any region. We can conclude that the smaller regions have to be rotations of one another and that each region has at least two protrustions. This means that for both regions we need to draw an extra protrusion and these need to be next to each other. Because the grid without the two known protrusions is only two squares wide, we know this will split the grid into two parts and it has to happen on the third row, because otherwise we have regions of unequal size. Of the two possibilities only one actually gives us two rotations of the same shape.


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