Magic Squares Download Page

Spreadsheets

This material was prepared on a Macintosh and compressed using Stuffit Version 5.02. Three versions are stored:

• BinHex (.hqx) Unstuffed files which can be opened on a Mac without an Expander. (Note: larger files have been made self extracting archives).
• Stuffed File (.sit). Smaller files which need an expander to open them. These files can NOT be expanded with earlier versions of Stuffit Expander. To unstuff the small files download from Aladdin Systems the free StuffIt Expander 5.1 for Macintosh or the Aladdin Expander 5.0 for Windows.
• Zipped Files (.zip) Files compressed with MacZip which (hopefully) can be unzipped on a PC. If you are a PC user and do this please report your experience to me.

The Spreadsheets

This Excel Spreadsheet analyzes Magic Squares up to order 9x9. You can type in or copy in a magic square from 3x3 up to 9x9. The underlying structure of the magic square is revealed when you type in the optimal test factors.

The square to be analyzed is placed in the top left corner of the test area (cells M4 to U13). There are sample squares of various sizes to the right to facilitate experimenting. These 9x9 areas may be directly pasted into the test area. If a small square is pasted in from elsewhere, the remaining cells will have to made empty (highlite and Command/B). After pasting in the Square to be tested, enter suitable divisors into squares D8 - D13, e.g., for a 9x9 - try 3,3,3,3,1,1; or 9,9,1,1,1,1. In general the smallest numbers are the best. Thus for an 8x8 try 2,2,2,2,2,2; and for a 5x5 try 5,5,1,1,1,1

The 9x9 spreadsheet opens with one Bree/Ollerenshaw 8x8 square - a type of Pan-Magic Square that does NOT have a Graeco-Latin Square as a basis. The divisors selected are the vertical yellow string of six 2's (D8 - D13). It is interesting to try other sets of divisors, e.g., 4,4,4,1,1,1; or 8,8,1,1,1; etc., to see different patterns. The spreadsheet is locked so that only the yellow squares can recieve input.

The 12x12 spreadsheet opens with an 11x11 pan-magic square being broken down into two Latin Squares, each with a different knight's move.

These spreadsheets do a lot of work. They check that the square contains one each of all of the numbers 0 to NxN-1. They check whether it is magic and the 9x9 version checks whether it is pan magic. They also perform similar checks on all the derived component squares - and list these properties beside your chosen test divisors.

Pan-Magic (Bree/Ollerenshaw) Square Creator

This Excel Spreadsheet is creates Magic Squares up to order 40x40. You enter a number between 1 and 10, and the spreadsheet automatically creates a square of order 4 up to 40. It automatically performs the conversions described by Bree and Ollerenshaw. Unfortunately, their own ebsite describing their technique no longer exists. The best description is currently provided by: Harvey Heinz

Marian Trenkler's Magic Cube Maker:

Marian Trenkler's formula is used in these two spreadsheets to make magic cubes. The smaller example makes a 3x3x3 magic cube, and the larger one makes a 7x7x7. All you do is enter the size of the square and the cells are automatically filled with all of the correct values.