Hashiwokakero

The logic game "Bridges", first published in Japan in 1990, is distinguished by simple and understandable rules, and at the same time - the complexity of the solution. The playing field “Bridges” has a rectangular shape and is divided into squares, in the center of which there are “islands” - circles with numbers.

As a rule, the square grid is either not drawn initially, or is erased after placing all the islands - in order not to interfere with the player drawing straight lines (“bridges”) between them. Lines can be drawn strictly perpendicular and horizontal (diagonally is prohibited).

The task that is set for the player is to connect the islands with bridges in such a way that the number of the latter corresponds to the digital values inside the circles. So, for an island with the number “3” three bridges should be built, for an island with the number “5” - five bridges, and so on.

In one direction - up, down, left and right - 1-2 lines can be drawn. Thus, the maximum number of bridges for each island is 8, and eight is the maximum allowed numerical value in the game.

General rules

Since the playing field is conventionally presented as a body of water with islands and bridges between them, the directions in the game also have geographical names: instead of “up, down, right, left” they say “north, south, east, west” " However, this does not apply to the mandatory rules, and players can give objects on the field (and line directions) any other names. The main ones remain four fundamental conditions:

• The number inside the circle should correspond to the number of bridges drawn to the sides of it.
• One or two bridges can be built between two circles.
• Lines between circles can only be drawn horizontally and vertically, without allowing them to intersect with other circles.
• It is not allowed that at the end of the game there are circles left that are not connected to any of the other circles.

A correctly constructed puzzle should consist of a network of bridges connecting all the islands on the map. That is, it must be possible to move from each island to any other - along conventional bridges. Separate islands not connected to bridges are not allowed!

How to solve the puzzle

The minimum number that can be placed inside the circle is “1”, and the maximum is “8”. Thus, the easiest one to solve is the last one. If you see an island with a figure eight on the playing field, you can safely draw two lines from it in each direction: north, south, east and west. No other options are possible here, according to simple and immutable mathematical rules.

But in the case of the seven, the task becomes more complicated, since one of the bridges must be not double, but single, and which one is unknown. The second simplest is the number “1”, from which you only need to draw one line - towards the neighboring island. But if there are several such islands, this move should be postponed until later. The remaining numbers - from “2” to “6” - are the most variable and difficult to solve, and it is with them (after eight) that you should start solving the puzzle.

General recommendations that should be followed to achieve a quick victory:

• Do not start the game by connecting twos and ones if there are more significant numbers on the field. First, it is recommended to build bridges for eights and sevens, and only then for other numbers (downwards).
• Building each bridge limits further steps and reduces the limits for neighboring islands. So, by drawing a straight line between “3” and “1”, you will reduce the remaining limit for the first digit to two, and for the second to zero.
• For the number "6" the same simple solution is often applicable as for the number "8". So, if the islands are located only in three directions from the six (and the fourth is empty), you can without hesitation draw double lines between them (3 × 2 = 6).
• Use the elimination method. For example, if there are four islands next to an island with the number “6” and one of them with the number “1” (with no alternative to connecting to other islands), after merging them, there will be “5” bridges left that need to be distributed among the remaining three islands. And if initially the option with three double bridges (2 × 3) was possible, now you can safely draw one line from the six in each direction.

These rules and tips may seem complicated in text form, but with a little practice in a real game, you will be convinced of their simplicity and effectiveness. Like many other Japanese puzzles, “Bridges” can captivate players seriously and for a long time, and you will spend more than one hour playing this pleasant and exciting entertainment.