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/