This is an example of a completed Shakashaka puzzle. The aim is to fill the grid with empty white cells and triangles so that all of the white areas form rectangles.

Some cells are black with numbers in them, this tells you how many triangles are next to this cell.

This is an example of a starting Shakashaka grid. The starting grid is mainly white, but with a small number of black cells. Some of the black cells have clues, this tells us how many triangles surround that cell.

I have highlighted two cells with a '3' clue. Let's look at the '3' clue on the right first. It tells us that there are 3 triangles surrounding this clue, and with only 3 available cells, we know that cells 'D', 'E' and 'F' must all contain triangles. We have 4 different types of triangles to choose from, but if we look at cell 'D' first, we can see that the only triangle that can fit here is a top-right triangle. Similarly for cell 'F', this cell must contain a top-left triangle.

Looking at the other '3' clue we are in a similar situation, we know that cells 'A', 'B' and 'C' must all contain triangles. The easiest cell to look at is cell 'A', where the only valid option is a bottom-right triangle.

We have inserted our triangles from the last step. We are now in a situation where we have 2 triangles against a 'black' wall, or the edge of the puzzle. We can imagine that the outline rectangle outline, will 'bounce' off these obstacles. Looking at the highlighted cell on the left, this means cell 'A' must contain a lower-left triangle, and cell 'B' must contain a top-right triangle.

We can apply the same logic to our other highlighted triangle, and say that cell 'C' must contain a top-left triangle.

We can also look at cell 'D'. There is no way to insert a triangle in to this cell - there would be no way to create a rectangle, there simply isn't the space. This means we can mark cell 'D' as being empty.

In the top-left of our puzzle we almost have a complete rectangle. The only option we have for cell 'A' is a top-left triangle.

If we look at the bottom of the puzzle, the highlighted '2' clue now only has two available cells next to it. The only available option for cell 'B' is a bottom-right triangle. Because of the black wall cells around it, the only option for cell 'C' is a bottom-left triangle.

Looking at the highlighted '2' clue in the top-right, we know that both cells 'D' and 'E' must contain triangles. The only option for both cells is a top-right triangle.

We now have a few situations where out rectangle outlines are hitting either the edge of the puzzle, a black wall, or an empty square. As we saw earlier, all of these will cause the rectangle outline to 'bounce' off the obstacle.

This means,

• Cell 'A' must contain a bottom-right triangle.
• Cell 'B' must contain a top-right triangle.
• Cell 'C' must contain a bottom-left triangle.
• Cell 'D' must contain a bottom-right triangle.
• Cell 'E' must contain a top-left triangle.

There are now a few empty cells we can fill in. I have highlighted the '1' clue in the top-right of this puzzle. This clue already has it's one triangle above it, which means that cell 'A' must be empty.

We can also look at cells 'B', 'C' and 'D'. None of these have space for a triangle, so they must all be empty as well.

We can also look at the highlighted '4' clue in the middle of the puzzle. All four cells around this clue must contain triangles, and there is only option for each cell. Cells 'E' and 'G' must contain top-right triangles. Cells 'F' and 'H' must contain bottom-left triangles.

One of the things we know about rectangles is that each side must have an opposite side. We know the two highlighted cells are one side of a rectangle, but we don't have other side. If we look at the sides of this rectangle we can see that cells 'A' and 'B' must be the opposite side here, i.e. cells 'A' and 'B' must contain bottom-left triangles.

Similar to previous steps, our rectangle outline 'bounces' off obstacles for cells 'C' and 'D'. This means that cell 'C' must contain a top-left triangle, and cell 'D' must contain a bottom-right triangle.

We can now return to the '3' clue in the top-left. We know that cells 'A' and 'B' must contain a triangle. With the empty cell now next to 'A' we know that cell 'A' must contain a top-left triangle. With the combination of black walls next to cell 'B', the only triangle we can insert here is a bottom-left triangle.

We can also insert an empty cell in cells 'C' and 'D', there is not enough space here for a triangle to be inserted in either of these.

We can now conclude that cells 'A', 'B' and 'C' make up a rectangle with the triangles that are already in place, i.e. cell 'A' must contain a top-left triangle, cell 'B' a bottom-right triangle, and cell 'C' a bottom-right triangle.

From the triangle we inserted last step, we can also insert a top-right triangle in cell 'D', and a bottom-left triangle in cell 'E'.

We can now conclude that cell 'A' must contain a bottom-right triangle to complete that rectangle. This means that cell 'B' must contain a top-left triangle, and that leaves cell 'C' empty.

We know that cell 'D' must contain a triangle (because of the '3' clue just above it), the only option that works here is a top-left triangle. This means that cell 'E' must contain a bottom-left triangle.

We can now look at cell 'A' and 'B'. If we were to insert an empty cell for cell 'A', that would also mean that cell 'B' would be empty. This would then leave us with a 'L' shape of empty cells, with a black wall making up the fourth corner. The aim of the puzzle is to fill the grid with rectangles of empty area, i.e. this would be against the puzzle rules.

This means that cell 'A' must contain a triangle, the only valid triangle is a top-right triangle. This would also mean that cell 'B' must contain a top-left triangle.

We also now know that cells 'C' and 'D' must complete the big rectangle in the top-right, i.e. cell 'C' must contain a bottom-left triangle, and cell 'D' contains a bottom-right triangle.

We can now insert a bottom-left triangle in cell 'A', and a bottom-right triangle in cell 'B' to complete that rectangle. The two cell under 'A' and 'B' will be left empty.

We can also insert a top-right triangle in cells 'C' and 'D' to complete that triangle. This leaves cell 'E' as empty.

We are now almost at the end of this puzzle. We have two options for cells 'A', 'B', 'C', and 'D'. If we closed the rectangle by placing a top-right triangle in cell 'A', that would leave cells 'B', 'C', and 'D' empty. This would not be a rectangle!

The only option left is to extend this rectangle a little further so that cell 'B' is a top-left triangle, cell 'C' is a top-right triangle, and cell 'D' is a bottom-right triangle.

Our finished Shakashaka puzzle!