One of the puzzle consists of a few points, and the question is, how many squares can you create by connecting 4 points together. Let's take a look at it. Yes, it is easy to see the small squares with an edge length of 1. And even the two other with and edge length of 2 are easy to find. But nearly nobody of the onlookers see the squares, which can be created by connecting points in an other angle than 90°. In this case there are 2 additional one in an 45° angle.

To demonstrate how the puzzle can be easily solved with an computer I've written a few lines of C-Code which can count the squares inside a textfile. The 'x' is used to mark the points.

xxx xxx xxxxxxxxxx xxxxxxxxxx xxx xxx xx xx xx xx xx xx xxx xxx xxxxxxxxxx xxxxxxxxxx xxx xxx Try to count the number of squares by hand first. Listing of the program result (4 coordinates and the result number): (2.0,-1.0), (1.0,-2.0), (2.0,-3.0), (3.0,-2.0) solution 1 (2.0,-1.0), (2.0,-2.0), (3.0,-2.0), (3.0,-1.0) solution 2 (2.0,-1.0), (1.0,-3.0), (3.0,-4.0), (4.0,-2.0) solution 3 ...... (3.0,-9.0), (3.0,-10.0), (4.0,-10.0), (4.0,-9.0) solution 281 (7.0,-9.0), (7.0,-10.0), (8.0,-10.0), (8.0,-9.0) solution 282 (8.0,-9.0), (8.0,-10.0), (9.0,-10.0), (9.0,-9.0) solution 283 The program says that there are 283 squares. Unbelievable isn't it. |

The programming language is ANSI-C.

The natural language is english.

OS independant.

Source-Code: square.c

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created with quanta 3.1, werner.ho(AT)gmx.de 2003-06-20