Ambigram Magic Squares

When using standard characters, the digits 0, 1, and 8 are symmetrical around the horizontal axis, while 6 and 9 are interchangeable when rotated 180 degrees.

With these digits, we can create magic squares that maintain their constant sum even when flipped, as illustrated below.

Interestingly, when these numbers are represented in LCD style, we can also include the digit 2, which resembles a 5 when inverted. This allows for the creation of magic squares with additional properties related to both 2D and 3D symmetry—whether flipped or mirrored—such as the remarkable example created by Chris Wardle.

This isn’t the first magic square to exhibit such fascinating properties; there are many variations out there. I encourage you to explore and discover your own creations online. If you have original ideas for magic squares with these unique characteristics, we would love for you to share them with us!

For those interested in learning more about the history and mathematics behind magic squares, check out this fascinating article from the Royal Institution: The Fascination of Magic Squares.

More links of interest:
[1] https://www.rigb.org/explore-science/explore/blog/fascination-magic-squares
[2] https://math.hmc.edu/funfacts/magic-squares-indeed/
[3] https://patcherymenagerie.blogspot.com/2019/07/magic-squares.html
[4] https://www.geeksforgeeks.org/magic-squares-fun-fact-and-more/
[5] https://mathcommunities.org/magic-squares/
[6] https://www.magischvierkant.com/links-eng/
[7] https://chelekmaths.com/2020/06/30/cracking-the-cryptic-joy-and-magic-squares/
[8] https://www.byrdseed.tv/magic-squares/

Magic Square for Gunners

A magic square is a grid where the sum of the numbers in each row, column, and diagonal is the same, creating a harmonious balance. A “geomagic” square, on the other hand, is a grid of geometrical shapes where each row, column, or diagonal can be assembled into an identical shape known as the “target shape”. Like numerical magic squares, all shapes in a geomagic square must be distinct.

Concept by Lee Sallows.

The postage stamp below, issued by Macau Post on October 9, 2014, pays tribute to Lee Sallows, the creator of geomagic squares.

Further reading.

The Puzzling Ramanujan’s Magic Square

As you maybe know, a magic square is a square divided into smaller squares each containing a number, such that the figures in each vertical, horizontal, and diagonal row add up to the same value.

In this particular magic square by Ramanujan, fields of the same color add up to 139. The first row – highlighted in the bottom-right magic square – shows his date of birth.

IXOHOXI Magic Square

The neat magic square featured on this stamp was created by Brazilian mathematician Inder Taneja. This square, called IXOHOXI magic square, not only shows common properties like other magic squares, as well as being pandiagonal, but also include extra properties such as symmetries, rotations and reflections.

IXOHOXI magic square

Continue reading “IXOHOXI Magic Square”