Physics & Math Puzzles

Pearl Vault Puzzle

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From Etsy: BUY NOW: Pearl Vault Puzzle

Pearl Vault Puzzle: a tetrahedron assembly of four identical pieces traps within a pearl. Three challenge aspects to this puzzle: 1) get the pearl out from the center, 2) explain the physics of how the disassembly occurs, and 3) reassemble- for which 3) might be the most challenging. Swipe for reveal and note the conservation of momentum aspect of the solution. Designed by Bruce Patterson and expertly produced by Pyrigan Puzzles. 

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Magnetic Cube

Many colors to choose from: 
From MagneticCube.com: BUY NOW Magnetic Dice Cube 

See also the original indestructibles post: Magnetic Acrylic Rubik's Cube 

Magnetic Cube: a twisty Rubik’s Cube puzzle made from 27 dice and 108 neodymium magnets. This cube includes the scrambled states and solutions of the original 3x3 Rubik’s Cube but is held together only by magnets! The magnets, in this special configuration, lock the dice together with a satisfying click upon rotation. This beautiful cube was produced by Owen Lillywhite of magneticcube.com and is based on a gfixler design posted on instructables.


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South Pointing Chariot

An excellent and affordable 3D printed version available here:
From Etsy: BUY NOW: South Pointing Chariot

Or get the files to print one yourself: From Printables: South Pointing Chariot 

Note: this site contains affiliate links for which I may be compensated

South-Pointing Chariot: no matter the direction carriage moves, or how many times it turns, the arrow remains pointing south (or whatever direction it was placed initially). This amazing mechanism utilizes a differential gear train, the famous device used in cars to allow wheels to rotate at different rates when cornering. Differential gear trains have the following property, the rotation rate of one shaft is equal to the average rotations rates of the other two shafts. Each wheel of this device drives one of two input shafts, with one geared in reverse, so that if the carriage is moving in a straight line the two rates average out to zero, and the output shaft connected to the top arrow stays stationary. If, however, the carriage turns a corner, one wheel then rotates faster, and the average rate then turns the top arrow at exactly the right rate to stay pointing in the same direction. This design is the most likely basis for the ancient (about 200 CE) Chinese South-Pointing Chariot, described in historical manuscripts which describes a statue on the carriage with an arm extended pointing South. This version was designed by software engineer and tinkerer extraordinaire Matt Keveney, and expertly printed by my friend Alex Kling. 

Chiral Aperiodic Monotile Puzzle

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From Etsy: BUY NOW: Specter Tile Set by Nervous Syestem

Note: this site contains affiliate links for which I may be compensated

Read the published paper: A chiral aperiodic monotile

Chiral Aperiodic Monotile: these puzzle pieces are all identical in shape, based on special family of forms called “specters”, and are key to a major mathematical discovery in May of 2023. Specters will tessellate a plane to infinity, similar to how squares or hexagons can tile out with no gaps. However specters are identically shaped tiles which fill the plane aperiodically- if one tries to shift a part of a specter tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! The fact that aperiodic tessellations exist at all is pretty amazing, and Sir Roger Penrose (Nobel prize in physics 2020) is also famous for discovering a pair of regularly shaped polygons in the 1970s that tile in this aperiodic way. Specters were discovered by the same team of mathematicians (Smith, Myers, Kaplan, and Goodman-Strauss) who discovered “the hat” aperiodic monotile in March 2023, but the hat needs its mirror image to complete the tiling whereas the specter does not. An amazing development found only two months after the initial major breakthrough. Credit to the @nervous.system design team for modifying the specter into an interlocking puzzle piece form- and assembling these without gaps is a fair challenge! 


Trisected Sphere Puzzle

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From Etsy: BUY NOW: Trisected Sphere Puzzle

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Trisected Sphere Puzzle: three identical pieces interlock to form a ball in this elegant 3D printed dissection puzzle. The sphere is sliced following a helical path from one pole to the opposite pole, creating a smooth disassembly and reassembly.

See other fun geometric puzzles here: dissection puzzles

Kluster Magnetic Challenge Game

Get this fun magnetic game here:

From Amazon: BUY NOW: Kluster Magnet Game

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Kluster Magnetic Challenge Game: explore mysterious action at distance via magnetic fields with this fun game setup. Note how the polished barium-strontium ferrite ceramic magnets repel each other when properly oriented, but once one flips over the unstable equilibrium gives way to the north/south attraction, and they quickly snap together. The game is played by taking turns placing the magnets within the boundary of the cord without any jumping together- the first to place all their magnets in the loop without any “clustering” wins, if some do cluster you take those magnets and lose your turn. Comes with the cord and a nice velvet storage bag.

Shashibo Puzzle Dissected

Get this cube puzzle (in a variety of colors and patterns) here:

From Amazon: BUY NOW: Shashibo Cube
From Art of Play: BUY NOW : Shashibo Geometric Art

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Shashibo Puzzle Dissected: I cut apart one of these puzzles to better understand the geometry: it is indeed a cube dissected into 12 equal irregular tetrahedra as seen here. The embedded magnets still allow construction of the cube. Of course the symmetrically placed hinges (along with strategically placed magnets) creates the real magic of the Shashibo puzzle- a device with more that 70 geometrically interesting and aesthetic configurations including a rhombic dodecahedron as well as the cube.


Symmetric Sticks Puzzle

Geometry as art and play-- get this affordable puzzle here:

From Etsy: BUY NOW: Symmetric Sticks Puzzle

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Symmetric Sticks Puzzle: 30 identical pieces, each with two notches as shown, can create 12 interlocking pentagons in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 4 others that connect with it. Precision notches on the rods allow them to interlock with elastic tension such that vector sum of the 4 forces sum to zero in this tensegrity type equilibrium. The dodecahedron, with its 30 edges and 12 sides, is the basis of this puzzle sculpture.

Shashibo Earth

Available here:

From Amazon: BUY NOW: Shashibo Earth
From Art of Play: BUY NOW : Shashibo Geometric Art

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Shashibo Earth: the globe of the Earth is mapped to a rhombic dodecahedron in this new design of the Shashibo shape shifting puzzle. Dissect a cube into 12 equal irregular tetrahedra, connect these pieces symmetrically with hinges and add 36 magnets to create the Shashibo- a device with more that 70 geometrically interesting and aesthetic configurations (a few are shown here as the dodecahedron is transformed to a cube).

Ambiguous Circles and Squares 

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From Shapeways: BUY NOW: 3D printed Illusions 

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Ambiguous Circles and Squares: two more examples of the Sugihara ambiguous object illusion, with “impossible” mirror reflection. Thanks to Gerardo Ortega for sending me these 3D prints of his designs.


Gravity Drop Challenge

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From Etsy: BUY NOW: Gravity Path Demo Puzzle

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Gravity Drop Challenge: starting at the same height, and ending at a same lower height, which path will take the shortest amount of time? The straight line (red marble) or the wavy longer path (blue marble)? The weird thing is that both marbles will have identical speeds at the finish line- yet one gets there quicker. The physics problem of finding the curve of fastest descent is called the brachistochrone problem- from the Greek words brakhistos ‘shortest’ and khronos ‘time’- and it is not a straight line. The fastest curve turns out to be the cycloid- a topic for a future post.

Aperiodic Monotile

Learn more about this recent math dicovery here: An aperiodic monotile (arXiv)

Althogh the math says they can tile the plane, getting them to do so is more challenging than one might think! 
Get a set of laser cut hat tiles here:
From Etsy: BUY NOW: "the Hat" monotile set

See other aperoidic tilings in my collection.

Note: this site contains affiliate links for which I may be compensated

Aperiodic Monotile: this newly discovered 13 sided shape, named “the hat”, will tessellate a plane to infinity, similar to how squares or hexagons can tile out with no gaps. However the hat tiles the plane aperiodically- if one tries to shift a part of a hat tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! The fact that aperiodic tessellations exist at all is pretty amazing, and Sir Roger Penrose (Nobel prize in physics 2020) is also famous for discovering a pair of regularly shaped polygons that tile in this aperiodic way. However it was not clear until a few weeks ago if a single shaped tile could tessellate aperiodically when the hat was described in a paper by Smith, Myers, Kaplan, and Goodman-Strauss uploaded to arXiv March 20. 

Puzzle Proofs

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From Etsy: BUY NOW: Puzzles from Jeux Efce

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Puzzle Proofs: three mathematical proofs in a physical form that use equivalent areas to make the case. The first video illustrates one of the most famous equations concerning the sides of any right triangle, the Pythagorean Theorem. The area of a square with side c of the hypotenuse is indeed equal to the sum of the areas of the squares of side a and b. One of the most used formulas when calculating vectors in physics classes! In the second video, similar comparisons of areas illustrate two special binomial products (a+b)² and (a+b)(a-b), and connects these famous algebraic equations to simple geometry.