# Order 5 Magic Squares

## Construction

Program Order5
makes the 275,305,224 order 5 magic squares.

## Squares

Here are the first and last 5x5 magic squares, (in
Frénicle standard form sorted in ascending order):

## Type Summary

This is the type summary from program GetType:

Note: Pandiagonal 1-way does not include pandiagonal.

## Groups

There are 101,774,553
complement pair pattern groups. The squares of 4,845,739 groups have center 13.
See all groups,
center 13 groups,
center not 13 groups.

## Counting the Squares

Order5count counts
the squares in 4 minutes on a personal computer at 3.0GHz, (see counting
detail):

### Computer

Manufacturer: Dell
Model: Alienware Area-51 R2
Processor: Intel® Core™i7-5960X CPU @ 3.00GHz 3.00GHz
Memory(RAM): 32.0 GB
System type: 64-bit Operating System
Windows edition: Windows 10 Home
Environment: Microsoft® Visual C++® 2010 Express Edition

## Cell Number Position Counts

The counts of squares for each cell number by position are:
.txt

For example, there are **35,472,326** squares with
**1** in a corner cell, another **35,472,326** squares
with **1** in a cell one in from a corner along a main diagonal,
**4,365,792** squares with **1** in the center
cell, and so on.

Since each number from **1** to **25**
is somewhere in every square, each row in the table totals
**275,305,224**.
The column totals, (including row 1 to 12 numbers twice), are
**275,305,224** multiplied by the number of green cells at the top.