Ultramagic Squares of Order 7 |
Files |
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. |
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. |
At the moment I only present two files. Please send me a mail if you are interested in all files. I just want to know which investigations you plan. |
The first file contains the 23581 squares with n(1,1) = 1 and n(2,1) = 43. |
squares-01-43.zip (168 kB) |
The second file contains the 23581 squares with n(1,1) = 44 and n(2,1) = 1. |
squares-44-01.zip (166 kB) |
Notice that the two files contain the same amount of squares. Does anybody find a reason for this equality? |
ultra-magic-7x7-01-43.txt (4123 kB) |
ultra-magic-7x7-44-01.txt (4123 kB) |
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