Shikaku Puzzles Solving Tips

Although we don't have a shikaku magazine at present, we do have lots of other great puzzle magazines available for purchase and download.

If you have come across shikaku - also called sikaku before - then you can skip this first paragraph, the instructions. They are very simple indeed: the grid must be divided into a series of rectangles, and each rectangle must contain exactly one of the numbers given at the start of the puzzle. The numbers indicate the total number of cells inside that rectangle. Thus an '8' has to be part of a rectangle with 8 squares in. At the end of the puzzle every cell will be in exactly one rectangle.

That's the rules, but what strategies are there for solving shikaku? As ever, let's look at the sample puzzle to the right.

The easiest solving method is to look for rectangles that are forced immediately. Look at the very first cell of the grid - row 1 column 1 (R1C1), which has a 3 in it. There is only one possible way that rectangle of three cells can be orientated, a vertical 1 across by 3 down (1x3) so a thick line can instantly be drawn around it.

One of the methods you will use most often when solving shikaku is to work out where at least some cells of a particular rectangle must be, even if you don't know the whole shape of the rectangle, and thus narrow down the options in the process. For instance, look at the 6 at the bottom right of the puzzle. It can either be a 1 x 6 or a 2 x 3 in one of two locations. Now all of these have a common cell, which is that immediately above the 6 (the column above), so that can be marked as part of the region. Similar logic can be used for the middle of the three 3's in the second row: the cell beneath the middle '3' must belong to that region.

Another useful strategy is to work out which cells can only be reached by one rectangle. Since every cell must be part of a rectangle, then if there is only one rectangle that can reach the cell, it must be part of that rectangle. Look at the cell at the top right of the puzzle. The only rectangle it can be a part of is the '4' at the top right, and can be marked accordingly.

Working through the possible shapes of the rectangles and their positions together with noting which cells must belong to a particular rectangle are usually all that is needed to solve shikaku. With some harder puzzles you might need to reason along the lines of "if this rectangle were the shape of the x, then there would be no valid combinations for adjacent region y, therefore this can't be x", in other words do some simple cross referencing; however in a fair puzzle you should never have to work through by trial and error so such if/then logic should be reasonably straightforward.

That's it for the shikaku tips, we hope you've found them useful.

Although we don't have a shikaku or sikaku puzzle magazine yet, we do have a large selection of other fantastic puzzle magazines to download.

Read more Puzzle Strategy Tips on a range of different puzzle types.

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