Category: Magic

Posted on

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/

Posted on

Impossible Escape: A Topological Illusion

This is a fun and surprising escape trick for kids and family, that uses simple props:

· 1 karabiner clip,

· 1 metal ring,

· 1 loop of cord.

To begin:

1. The ring and the green karabiner clip are securely attached to the cord and cannot be removed.

2. Now, watch closely as I attach the green karabiner to the metal ring, making the setup even more complex.

3. Surprisingly, I can now simply pull the cord free.

Can you believe your eyes? Let’s try it together!

More topological magic tricks:

– https://archimedes-lab.org/2021/06/29/magic-topology-2/

– https://archimedes-lab.org/2020/06/09/magic-topology/

– https://archimedes-lab.org/2017/12/14/how-to-magically-untie-a-shoelace-double-knot/

Posted on

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.

Posted on

Impossible Paper Turn-up

Let’s explore a captivating paper-folding puzzle, part of the impossible origami family. It is simple to carry out and can be done at any moment.

Cut a 10-centimeter-wide strip from a two-colored sheet (in our case, yellow and red). Make sure the paper strip is at least 24-25 cm long! By gluing the ends together, you may turn this strip into a ring, as shown below. The goal is to create a turn-up in the ring without tearing it… Impossible? Many of your friends will attempt, but the outcome will always be negative.

This is how the trick works:

Flatten the paper ring and fold the top edge by 2-3 cm (see fig. 1). Unfold only the single top layer of the fold, creating two triangular folds at each corner of the flattened ring (fig. 2). Next, fold the two outer edges along the base of the flattened triangles (fig. 3). Then, fold the outer edge upstream. This way, a folded edge is now on each face of the flattened ring.

Now, insert your fingers inside the ring, firmly holding one corner between your thumbs and index fingers. Carefully separate your hands, pulling the sheet at the corner, releasing the excess paper hidden between the folds (fig. 5a and 5b). Repeat on the other corner. Finally, rearrange the paper ring, smoothing out the visible folds. The top edge of the ring is now completely turned on itself, creating a perfect turn-up without tears. Who would have thought? Congratulations, magician!

Posted on

Amazing Disentanglement Puzzle

How to transform ordinary rulers into captivating feats of magic? Equip yourself with two standard 30 cm rulers, made of wood or other materials. Attach a 20 cm string to each ruler by threading it through the hole at one end (see Fig. 1). Form a cord loop around one ruler, knotting the loose end of the cord, as depicted in figures 2 and 3. Ensure the string ring is not too tight, allowing it to glide smoothly along the ruler.

Repeat with the second ruler, threading the cord through the loop of the first ruler, as shown in figure 4.

The challenge is to separate the rulers without cutting or unraveling the cords. Despite the apparent difficulties, the solution unfolds seamlessly.

This string puzzle can also be build using two plastic pipes and two curtain rings (see figure 5).


show solution

Posted on

Illusory Geometry with Dice

Forced perspective is employed to craft a well-known object: the ‘tribar.’ Emerging from an “impossible catalog,” this object takes the form of a triangular structure, with square-section bars seamlessly joining at right angles. Constructing a tribar within three-dimensional space is an illusion; in Euclidean geometry, the sum of triangle angles always equals a flat angle.

Efforts to fashion a solid object resembling the tribar have met varying degrees of success. In this instance, our construction incorporates a deliberate ‘interruption’ that, when observed from a specific angle, creates the illusion of a complete triangle.

Consider fourteen dice. Sacrifice one by cutting to detach two faces (fig. a). Adjoin the remaining dice by gluing them together (fig. b), and affix the two faces of the truncated die onto the vertical stack of dice, as shown in fig. c.

© G. Sarcone – from the book Optical Illusions.
Continue reading “Illusory Geometry with Dice”
Posted on

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.

Posted on

Paradoxical Elastic Squares

A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?

Paradoxical Squares

This puzzle is available as greeting cards from my online store.