ultramagic squares of order 7

Ultramagic Squares of Order 7

Files

Structure of a data-file

There exists one data-file for each partial task. This makes 90 files. The avarage file-size is about 500 kB (unpacked). The files contain normal text. Each file has a header of four lines. For example:

Magic Squares Data by Walter Trump 2001

The first line may be ignored.

Typ=7x7-01-35

The second line discribes the types of the listed squares, especially the numbers in the cells (1,1) and (2,1). The example contains all pan-magic self-complementary 7x7-squares with number 01 in cell (1,1) and number 35 in cell (2,1).

Num=0053394

The third line tells us, how many squares are listed. This should be the total number of all squares with the before mentioned properties.

Crc=01058314366

The crc-number (cyclic redundancy check) in the fourth line allows to verify the square-data. Permutations of the square-data have no influence to the crc-number. But deleting a square or changing any number in a square or permutating numbers in a square lead to a different crc-number. Notice that these special crc-numbers could only be used with the programming language GB32.

Data-structure of a single square

A square could be described by a set of only 12 numbers. Each first 6 numbers of row 1 and of row 2. All other numbers can be calculated very easily using the described equations.

The numbers were represented by letters. For instance:

AoBPgqihfvCD

The upper-case letters A, B, ... X represent the numbers 1, 2, ... 24.
The lower-case letters a, b, ... x represent the complementary numbers 49, 48, ... 26.
The number 25 cannot occure among the 12 numbers, because it is in cell (4,4).

How can you get the number corresponding to a given letter?
Formula for upper-case letters: n = Asc(Letter) - 64
Formula for lower-case letters: n = 146 - Asc(Letter)
No letter may occure twice in a single square-data-line, not even in a different case.

Download all essentially different squares in the formatting described above

ultra-magic-7x7-data.zip (23 MB)

Download two types of squares as unzipped plain text files

The first file contains the 23581 squares with n(1,1) = 1 and n(2,1) = 43.

ultra-magic-7x7-01-43.txt (4 MB)

The second file contains the 23581 squares with n(1,1) = 44 and n(2,1) = 1.

ultra-magic-7x7-44-01.txt (4 MB)

Notice that the two files contain the same amount of squares. Does anybody find a reason for this equality?

Download all essentially different squares as zipped plain text files

ultra-magic-7x7-01-xx.zip (81 MB)

ultra-magic-7x7-xx-01.zip (61 MB)

Index

summary	cells	equations	transpositions	improvements
results	programs	files	conclusions	samples