Ultramagic Squares of Order 7

I still don't know which details of my programs I will make available for the public. It would be necessary to add more comments to the code. There are also some new ideas, that could lead to improvements in the programs. I wonder if there is anybody interested in the details at all. Please send me a mail if you want to see the source-code of the programs. Two other magic-square-calculations are available without any restricton on my GB32-Site.

Programming-language GB32
The programs are written in GB32. This is a german programming-language that is also available in english language. It is absolutely excellent with respect to mathematical problems. You can download a trial version from gfa.net.

The number of each cell is represented by an own variable. For example: i34 describes the number in cell (3,4). This works faster than using an array i(x,y).
The array st( ) contains the 'status' of the integers -24, -23, ..., 24.
st(12)=0 means that the integer 12 is already in use.
st(12)=1 means that the integer 12 is available.

At the start of the program each cell-variables are empty. Then one cell after the other is filled with an available integer. The status-value of this integer is set to 0 (not available). It is very necessary to prove suitable equations with the numbers in the already filled cells as early as possible. If an equation is not fullfilled, we go one step back (backtracking), make the last integer available again and fill another integer in the actually considered cell.

I worked with up to 20 computers (550 MHz Pentium III). They needed about four days, but several tasks were done twice.

summary cells equations transpositions improvements
results programs files conclusions samples

Walter Trump, Nürnberg, Germany, (c) 2001-04-25 (last modified: 2004-06-27)