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 Spiel: Vierdimensional

Beschreibung für das Spiel Vierdimensional

Das in Windows integrierte Spiel "Minesweeper" dürfte wohl jedem bekannt sein. Hierbei müssen in dem Feld versteckte Minen zuerst lokalisiert und danach alle übrigen Felder aufgedeckt werden, um zum Ziel des Spiel zu kommen. Dieses Spiel funktioniert nach demgleichen Prinzip, wobei das Spielen mit vier Dimensionen einiges logisches Können voraussetzt.

Anleitung für das Spiel Vierdimensional



The game is similar to very well-known MINESWEEPER game which installs automatically with Windows. I suppose you already know the rules, here are they in short: clicking on a cell "opens" this cell and if there is a bomb there, you lose, if there is nothing there, a number appears on the cell, showing how many boms are near that cell. If there are no bombs nearby no number appears and additionally the whole area of empty cells and the borders of this area are opened. If you suppose there is a bomb on some sell you mark it with right-click.

In this game the field is 4-dimensional, and everything else is absolutely the same. It is usually hard to understand what a"4-dimensional field" means, so go on to the next section.


There are lots of explanations on the web what a 4D cube is, but since no one still knows what it is I will have to explain it, too. Imagine a 3D cube. It has height, length and width. These are 3 dimensions. Then imagine a line of cubes. Say, we had a cube 4x4x4 and now we have 4 cubes put in a line, each 4x4x4.

If each cell of the first cube has it's "brother" in the second, in the third and in the forth cube, we can "teleport" from a cell in the first cube to the corresponding cell in the second cube. Then, from that cell in the second cube, we can teleport back to the first cube or to the corresponding cell in the third cube. From the third cube we can teleport to the forth cube or back to the second.

For example, if we are now in point (1;4;3) in the second cube, we can teleport to (1;4;3) in the first cube or to (1;4;3) in the third cube.

As you might have already understood, we move along the forth axis, which can represent time or something else. We say, it is time.

Now look on the game screen: there is a table of squares. Each square is a stock. A column of squares is a cube 4x4x4.

Then, four columns show the four cubes we were talking above. We get 16 squares, representing states of 4 stocks of a cube at 4 different points in time or in four different worlds: astral, spirit, ethereal, material ;-)


In minesweeper for Windows each cell could have up to 8 heighbours. Usually it had 1, 2, or 3, but in crowded areas it could have even 8. That meant all cells around the cell we clicked on are bombs.

You would be surprised to know that in 4D there can be as much as 80 neighbours for one single cell.

In 2D the number of neighbours is (3*3) - 1 = 8; (The square 3x3 without the center cell)

In 4D the number of neighbours is (3*3*3*3) - 1 = 81 - 1 = 80; (The hyper-cube 3x3x3x3 without the center cell).

So, do not be confused if you see a number like 12 on some cell. The place is not at all overpopulated.

To make life easier neighbour cells of the cell you have your cursor over are highlighted. After you move the cursor around a bit, you will at some point understand what the **** it is: so much neighbours, it is impossible, the game is not for a human! The nighbours are not only in this square, but they are also in all 8 squares around..

Actually it not so hard, at least when on a large 4x4x4x4 field there are only 3 bombs - this is the easiest level of difficulty, needed just for general understanding of the game. Try to beat it, and you get the idea.


In minesweeper for windows we clicked on the cells like robots: no one needed to think, because nearly in all cases it was obvious where to click next.

In this game you must have high IQ :-) and good logic just to make a few secure clicks. On the medium difficulty level it usually takes about a minute to make a few successful clicks.


- click somewhere close to the side or to the edge to open a large empty area. Without it nothing works.

- search for "edge bombs". That means there is a cell with "1", and when you move your cursor over it, you see that there is only one unopened highlighted cell near it. Highlighted cells have red frames, and if the cell is unopened and highlighted, its field is yellow. So, "edge bomb" must be on that yellow cell, if you moved the cursor over "1" and saw a single place where a bomb can be. Mark it (right-click).

- If you marked some cell as a bomb, you get an advantage: now you can securely open all cells, which obviously are neighbours of this only bomb and not other bombs. The process may be familiar to you from windows minesweeper.

- If there are no edge-bombs, you will have to use another trick: find some cell with a number and some unopened neighbours. For example, you move the cursor over a cell with "1" on it, and there are 2 unopened neighbours near it. That means the bomb is in one of these cells. Then, say, you move the cursor to a neighour cell with "2" and see, that this cell has the same unopened neighbours, as the cell with "1" and one more unopened neighbour. Analyse the situation: cell with "1" has two candidates for a bomb, cell with "2" has the same two cnadidated and one more candidate. If the first two candidates contain one bomb it is logical for the third candidate to have a bomb, otherwise the cell with "2" would have "1". So, you can mark the third candidate as a bomb.

This last trick will give you the ability to beat a 10-bombs field. To feel comfortable with it you need some practice, of course.

Still, a 20-bombs field (hardest difficulty level) is not so easy to beat even if you master all the tricks described above. I have never beat it yet, beacause at some point of the game I usually noticed that my brain was aching, and my calculation abilities were not enough to remember how many bombs must be on different groups of cells.


Although gameplay of this applet is bad and the difficulty is too high, few people will play it. It may be interesting for mathematicians and maybe some puzzle-fans.

It is possible to make a 5D and 6D Minesweeper, even a 10D minesweeper. And, say, if we have a 4x4x4x4x4x4x4x4x4x4 filed there can be up to 3^10-1= 59048 neighbours. And it can be still shown on a very large 2D screen if we build table (10D) of tables(8D) of tables(6D) of tables(4D) of squares(2D) of cells.

Autor: Igor Galochkin (iseeall@narod.ru)

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