Physics & Math Puzzles

Soma Cube

The Soma Cube is available in a variety of materials and colors:

From Amazon: BUY NOW: Soma Cube

From Etsy: BUY NOW: Soma Cube

Soma Cube: Math toy invented by Danish scientist and artist Piet Hein, who claimed that this puzzle idea came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg (yes- that Heisenberg) in 1933. The seven pieces are all the ways 3 or 4 cubes can be joined, such that each piece has at least one inside corner. Amazingly there are 240 ways to make the larger cube from these 7 pieces- still not that easy! 

Frabjous Geometric Sculpture Puzzle

Get one here- five colors to choose from:

From MoMath: BUY NOW: Frabjous Sculpture Puzzle

Frabjous Geometric Sculpture Puzzle: 30 identical laser cut acrylic pieces interlock into 12 interconnected five point stars (each with a spiral vortex center) in this puzzle based of the Frabjous sculpture by artist and professor of mathematics George Hart (Prof. Hart is now on Instagram, follow him at @george.hart.sculptor to see more of his amazing work.) Note that if one connects the tips of the stars one gets the outline of a dodecahedron, with its 30 edges and 12 sides, and if one considers the face planes of the linked pentagrams the underlying shape is a polyhedron called the “great rhombic triacontahedron”. A year or so ago I got to visit the National Museum of Mathematics in NYC where I bought this puzzle in the @momath1 museum shop. This puzzle was great fun to assemble- buy one to support this inspirational museum, and make a great sculpture for your bookshelf! 

Nova Plexus Tensegrity Puzzle

Precisions machined and available in brass or stainless steel:

From Art of Play: BUY NOW: Nova Plexus Puzzle

Nova Plexus Puzzle: 12 identical brass rods can create 4 interlocking triangles in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 5 others that connect with it. Precision machined notches on the ends of the rods allow them to interlock with elastic tension such that vector sum of the 5 forces on each rod is zero- creating this astonishing geometry as the equilibrium state. Unlock the ends of any two rods and the system instantly disassembles (swipe to view process in slow motion). Invented/designed by artist and computer scientist Geoff Wyvill in 1978, this puzzle has just recently been made available for sale with a limited production run.

Magic Sand Wand Puzzle

This puzzle was produced in the 1990s, sometimes found on eBay (currently two avialable):

From eBay: SEARCH NOW: Magic Sand Wand Puzzle

Wikipedia has a good introduction to the possible mechanisms of the Brazil nut effect 

Magic Sand Wand Puzzle: this week’s physics brain teaser- move the steel ball through the sand to the other end of the tube. Amazingly it can be done in less than 6 seconds! Hint: spinning won’t help this time. The solution to this vintage puzzle relies on some interesting physics concerning granular convection. Answer below and swipe to reveal solution. 

Stomachion Puzzle

Get this 3-color laser cut acrylic version here:
From Kadon Enterprises: BUY NOW: Stomachion Puzzle

Also a very nice multicolor acyrlic version here:
From Etsy: BUY NOW: Stomachion Puzzle

Learn about the 1998 discovery of the lost writings of Archimedes (and the technology used to recover them) in this TED talk

Ancient Stomachion Puzzle: the oldest known puzzle, discovered in the writings of the great Greek physicist and mathematician Archimedes from some 2200 years ago. The puzzle is a dissection of a square into 14 polygons, where the areas of each piece are integer multiples of each other (a curious way to slice it up). In 2003 Bill Cutler showed that there are 536 district ways to configure these pieces to make the square (five are shown here), ignoring simple rotations and reflections. Swipe to see the most famous solution, attributed to Archimedes himself, that was found in an ancient manuscript discovered only in 1998- before this date historians knew the name of the puzzle, but no one knew what it looked like. Kate Jones, the maker of this particularly aesthetic version, found that when using only three colors for the polygons, there are only 6 solutions where no two pieces of the same color touch (four solutions shown here).


Get the full version (8 disks made of wood) or the mini (6 disks, blue or red plastic): 
From Amazon: BUY NOW TrueBalance Coordination Puzzle 

TrueBalance: coordination challenge puzzle- get the six disks, connected by bearing swivels, into a vertical stack by only tilting the handle. Harder than it looks to get each disk’s center of mass above the one below at the same time into the unstable equilibrium final state. The swivels constrain the system, limiting the degrees of freedom, and allowing strange and interesting motion. Kinetic art as a toy! 

Balance Stacking Sculpture

Another wonderful desing by BinDesign- get one here in black or natural wood:

From Etsy: BUY NOW: Bin Design Balancer Puzzle

Balance Stacking Sculpture: a series of torques in unstable equilibrium complete this Calder-esque structure. As each component is added its weighted end balances all the others before it, with the initial small piece weighing about a gram or so. Remove the end piece and the whole structure comes down. Another wonderful design by artist Bin Xu.

Pythagorean Puzzle

Available here: 
From Creative Crafthouse: BUY NOW Pythagorean Puzzle

Pythagorean Puzzle: a proof, in physical form, of one of the most famous equations concerning the sides of any right triangle. 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. This kit also allows at least two other ways to prove this theorem named after the famous Greek mathematician from 500 BC. One of the most used formulas when calculating vectors in physics classes ?

Impossible Wallet

Available here: 
From Amazon: BUY NOW Magic Wallet 

From eBay: BUY NOW Magic Wallet

Impossible Wallet: this pocketbook has a special double hinge that allows the wallet to be opened from either side, and leads to some rather nonintuitive consequences. Note that once inserted, the bill shows the same face independent of which way the wallet is opened. The construction of this magic (or flip) wallet is similar to the famous Jacob's Ladder toy.

Impossible Pipe Elbows

These are very hard to find- I had to make this one. Contact @physicsfun via DM if you really want one.

Many other types of impossible objects are avialable- see these links and videos: Impossible Objects

Impossible Pipe Elbows: made from standard pipe fittings held together only by their threads. No glue of any kind was used in its making. Design inspired by puzzle maker and artist Saul Bobroff.

Impossible Dovetail

Inexpensive versions of this "impossible box" like that in the video avaiable here:

From Amazon: BUY NOW: Impossible Box Puzzle

Impossible Dovetail: this impossible object is pretty common, but it is a classic, and included in my collection. If one assumes a regular dovetail joint then this construction would indeed seem impossible without cutting and gluing, but what one sees from the sides makes for misleading assumptions as this box opens easily. Swipe for reveal once you’ve thought about about possible constructions. 


These dice are available here:

From Amazon: BUY NOW: Rock Paper Scissors Lizard Spock Dice

RPSLK Dice: the famous Lizard Spock extension to the Rock, Paper, Scissors game expressed on 10 sided dice allowing the study of the non-associative nature of the game (Rock wins Scissors, and Scissors wins Paper, but Rock does not win Paper, etc.), and other interesting math. The original RPS game had three “weapons” and only three rules are needed to play the game. Adding Lizard-Spock makes for 5 gestures, but now 10 rules must be used, including “Spock vaporizes Rock”, “Lizard poisons Spock”, and my favorite “Paper disproves Spock” (swipe to see famous graphic). Interestingly, mathematical analysis shows a similar four weapon game with equal odds of winning is not possible. It was also found that the next possible game with 7 gestures would require 21 rules to play. The Lizard-Spock extension was invented by Sam Kass and Karen Bryla in 2005 and made famous on the sitcom Big Bang Theory. 

Sphere Sticks Geometric Puzzle

Get this affordable and amazing puzzle here:

From Etsy: BUY NOW: Sphere Sticks

Sphere Sticks Puzzle: 30 identical wood 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 cut 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. 


Rhombic Blocks Mathematical Puzzle

This beautifully made puzzle available here:: 
From Etsy: BUY NOW 
Rhombic Blocks 

Rhombic Blocks Mathematical Puzzle: There are 9 possible ways three rhombuses can be joined together along a common edge, and similar to pentominoes, these 9 tri-rhombs can tile a polyhedron, in this case a hexagon. There are 14 solutions to this puzzle, and one where no same-colored pieces touch. A beautiful math discovery by puzzle master Stuart Coffin.