Shikaku

Shikaku is played on a rectangular field, most often a square one. The larger it is, the more difficult it is for the player to find the right solution.

Like many other Nikoli puzzles, Shikaku is classified by difficulty. While even a child can cope with small puzzles, solving large ones takes a lot of time even for adult intellectuals. However, this process is greatly simplified if you know the rules and follow winning strategies.

Basic rules

The Shikaku puzzle has simple rules that you can figure out in a couple of minutes. On a rectangular field, divided into square cells, there are numbers, which are always significantly smaller than empty cells. The player’s task is to form rectangles around these numbers so that the number of their cells corresponds to the values of the numbers. So, the number 4 should be inscribed in a rectangle of 4 cells, the number 7 - in a rectangle of seven cells, and so on.

The basic game rules that every player needs to remember include the following:

• Each rectangle must contain only one number inside.
• The number must exactly match the number of cells that make up the rectangle.
• The intersection of two rectangles is not allowed.
• At the end of the game there should be no free cells left on the field. All of them must be assigned to one or another circled rectangle.

Construction of complex figures is not allowed in this game. Only rectangular shapes without protrusions beyond the planes are allowed. For example, valid rectangles are 1x2, 2x2, 1x7, 2x5. Moreover, their numerical value must strictly correspond to the product of length and width, that is, area. For 1×2 it is two, for 2×2 it is four, for 1×7 it is seven.

How to solve the puzzle

Having remembered the basic rules, you can begin solving the puzzle. You should start with small playing fields, and only then move on to larger ones (10x10 or more). In any case, the tactics will boil down to finding and tracing the desired rectangles around the numbers scattered across the playing field.

The simplest and most uncontested option is numbers with a face value of “1”. You can immediately draw lines around these cells. But in the case of other numbers, you will have to rack your brains a little.

To quickly achieve victories in Shikaku, follow these tips:

• The width of rectangles containing prime numbers is always one. The simple ones include: one, two, three, five, seven, eleven, thirteen, seventeen, nineteen. That is, numbers that are divisible only by themselves and one. It is impossible to construct a rectangle with a width of more than one cell from them!
• If a number is a perfect square (4, 9, 16, 25, 36), a square shape can be formed around it with a side equal to the square root of that number. So, around the number 4 you can form a 2x2 square, and around the number 25 - a 5x5 square.
• If a number has more than two divisors, there are several options for the size of the rectangle that contains it (its width may differ from one).

The vast majority of rectangles on small-sized Shikaku playing fields have an elongated shape and are only one or two cells thick. Squares are less common, as are rectangles with a thickness of more than two cells. The player’s task is to find uncontested options and draw lines around them. This will require logical thinking and the ability to use the method of mathematical deduction.

After playing a few games of Shikaku, you will be convinced that this simple game is so exciting that you will want to play it again and again.