THE ASSISTED
8-PUZZLE GAME.
First of all, we must know what the 8-puzzle game
consists of; we go to the Help menu, located in the upper left corner of the
game window, and select the Clues option. A window appears that contains a
table of key concepts and their definition. The following definition is
provided in the "GOAL CONFIGURATION" entry: "The objective of the
8-puzzle is to rearrange a given initial configuration of eight square tiles on
a 3 x 3 board, numbered from 1 to 8, into a specified goal configuration "
The rearrangement of the tiles is carried out by successively sliding tiles
into the orthogonally adjacent empty square. Sliding a tile in the empty square
is called "STEP". In the game there are two possible goal
configurations:
One of the two goal configurations
is the current one, which must be reached by moving the tiles. An image of the
current goal configuration (CGC from now on) located in the upper right corner
of the game window reminds us constantly. Later we will see how to change the
CGC to the other available configuration.
The assisted 8-puzzle game window
has two clearly differentiated zones. In the zone of the left the board with
the tiles is represented; and in the one on the right is the step indicator disc.
The indicator disc has 32 numbered positions from 0 to 31, and consists of an arrow that always points to one of the positions. The number of the position
indicated is the minimum number of steps to reach the CGC from the current
configuration of the tiles on the board. The arrow will change its position
for each step we make on the board.
At the top left of the indicator disc
there is a three-digit counter. This counter indicates the number of steps the
player has taken when moving the tiles of the board from the initial configuration
to the current configuration.
On the indicator disc there is a
red dot that is placed next to one of the positions. This point does not change
position during the game; Its purpose is to indicate the minimum number of
steps to reach the CGC from the initial configuration of tiles of the board.
Comparing the value indicated by
the red dot and the total of the sum of the values of the arrow and the
counter of the indicator disc, we obtain the deviation of the optimal way to
reach the CGC of the game.
In the center of the indicator
disc there is a selector that serves to open or close the indicator disc. When
the indicator disc is opened, the positions are activated and become
selectable. The selection of one of the positions causes the loading of a new
configuration of the tiles on the board; in this way the distribution of the tiles
is such that it verifies that the number of the position selected in the
indicator is the minimum of steps to reach the CGC from the configuration of
the board that has been loaded. It is a way to start the game with a board
configuration of which we know the minimum number of steps to reach the CGC.
When selecting the position of the number zero the game board is loaded with
the CGC. And if we double click on the position of the number zero, the CGC of
the game is changed to the other possible, and at the same time the board is
loaded with a new initial configuration.
Another way to start the game is
to enter the eight tiles of the board one by one. We have this game feature
available when opening the indicator disc; Once opened, we have to go to the
Help menu, and select the option "Enter initial tiles configuration ".
Then a new window is shown, the distribution window, which has two boards. The
board on the right contains the cards distributed in the order of the CGC. And
the one on the left is empty. Dragging the tiles to the empty board we can go
placing the tiles with the distribution that we prefer. When we have moved the
eight tiles to the board, an icon will appear that indicates if the
configuration entered is valid. Only half of the configurations of all possible
ones are valid. A configuration is valid if it is possible to reach the CGC
through a successive series of steps. When a configuration is valid, a number
is displayed next to the valid configuration icon. This figure is the minimum number
of steps to reach the CGC. If we close the distribution window when the
distribution of the tiles is valid, this distribution goes to the game board as
the initial configuration of the game. In any other case, the game board will
maintain the configuration it had before entering the distribution window.
The assisted 8-puzzle game has
two functions that can be activated from the Help menu by selecting the Game
setup option. The configurable functions are:
- Anticipation of movement.
- Exclusion of the return movement.
The anticipation of movement
consists of three digits that appear below the indicator disc. The sum of the
three digits is always four, which is the number of possible moves in any
configuration of the board. The digit that is inscribed within the green circle
gives the number of movements that imply an approach to the CGC. The digit that
is inscribed within a red triangle gives the number of movements that move us
away from the CGC. And the one that is framed blue gives us the number of
neutral movements, that do not approach or distance the CGC.
The exclusion of the return
movement is characterized by the appearance on the board of a red tiel. This red
tile is displayed when the player tries to move the tile that moved in the last
step. The exclusion is equivalent to preventing the return to the last board
configuration before the current configuration.