Matchstick Puzzles

Matchstick puzzles are a set of visual puzzles that require you to re-arrange an arrangement of matchsticks into some new formation. The re-arrangement is bound by certain rules or limits and (usually) requires some lateral thinking to arrive at the solution.

When I was a teenager, my uncle, who was visiting us from France at the time, introduced me to my first matchstick puzzle. Having heard of my love of puzzles, he was keen to keep me (and himself!) entertained. At a family barbecue he pulled out a pack of toothpicks (not enough matches around!) and arranged 15 of them like so:

Matchstick Puzzle

(click the picture for a larger view)

He then asked me to remove three matches & what should remain is three squares. Remove three matches. No more, no less.

It took me roughly 15 minutes of off and on experimentation before I arrived at the solution. Try it yourself!

If you get stuck, click here for the solution.

If you liked that one, try the following three matchstick puzzles. They are among my personal favorites and can all be found in Martin Gardner’s “The Colossal Book of Short Puzzles and Problems”

Matchstick Puzzle

Move one match to form a square


Matchstick Puzzle

Move three matches and make the fish face the opposite direction


Matchstick Puzzle

Move one match and make the giraffe face right instead of left


hromanMatchstick Puzzles

The Apocalyptic Magic Square

Clifford A. Pickover’s book, “Wonders of Numbers,” was dedicated not to a person but rather to “an amusing mathematical wonder”

The Apocalyptic Magic Square

The Apocalyptic Magic Square is a 6 x 6 square grid of prime numbers where each row, column, diagonal, and broken diagonal sum to 666

hromanThe Apocalyptic Magic Square

The Fractal Curve

“At the earliest drawings of the fractal curve, few clues to the underlying mathematical structure will be seen”
-Ian Malcolm, Jurassic Park

Jurassic Park Dragon Curve

Jurassic Park Dragon Curve

Fractal Step 1

Fractal Step 2

Fractal Step 3

hromanThe Fractal Curve

Introducing Little Baby Hera

Born on Sunday, September 14, 2014 at 6:05 am

hromanIntroducing Little Baby Hera

The Ambigram

My answer to that ubiquitous question “What do you want to be when you grow up?” was always “a Doctor or Martin Gardner” (with the usual follow up “you know, the famous puzzler, mathematician, essayist, magician, and writer extraordinaire??”)

David Suzuki once did a “Nature of Things” documentary on Martin Gardner entitled “Mathe-magic.” The 1 hour special was fascinating beyond my imagination, with discussions about the mathematics of juggling, John Conway’s “Game of Life,” hexa-flexagons, and myriad other mathematical simulacra. (you can actually watch/download the documentary here.)

In one of the introductory scenes, a puzzle designer named Scott Kim began drawing the the first name “Martin” in a fancy script. When he finished, he rotated the paper over 180 degrees, and it read “Gardner.” In-frieking-credible.

Martin Gardner Ambigram

I would later learn text like that was called an AMBIGRAM1 – a word or phrase that can be read in more than one way or from more than a single vantage point.

Peter Newell’s “invertible illustrations” were sort of the precursor to ambigrams (Mental Floss has a nice collection of some of Newell’s work here). The last page in his first book of illustrations, Topsys & Turvys, reads “the end” but also when inverted reads “puzzle”:

THE END and PUZZLE optical illusion

And, ambigrams have shown up in a lot of pop culture over the years:

Ambigrams in Pop Culture

A 3-D ambigram on the cover of Godel, Escher, Bach by Douglas Hofstadter; and, rotational ambigrams on the covers of Dan Brown’s Angels & Demons and the special anniversary edition DVD of The Princess Bride

The other day, I re-discovered Erich Friedman’s page of wonderful ambigrams, which can be found here.

Remembering that Martin Gardner documentary, I became inspired to try my hand at an ambigram of my own name and doodled on scraps of paper for what seemed like hours… But, I eventually came up with something. So, here’s my name in two images one of which is just the other but rotated 180 degrees:

ambigram ambigram

Before I could develop an addiction (and start drawing everyone’s name I knew in similar fashion), I did some quick google/flickr searches and the results were disheartening – so many talented, imaginative folks out there.

  1. the term “ambigram” looks like it originated with Douglas Hofstadter []
hromanThe Ambigram