Physics & Math Puzzles

Pentominoes 3 Color Challenge

@physicsfun exclusive design- available only from STEMCell Science:

From Etsy: BUY NOW: 3 Color Pentominoes Puzzle

Pentominoes 3 Color Challenge: fit all 12 pentominoes into a 6x10 rectangle such that no two identically colored pieces touch. Pentominoes are the set of all 12 possible arrangements of five identical squares joined edge to edge. Since 5x12=60, the pentominoes can tile a 6 x 10 rectangle with no gaps (there are 2339 ways to do this- yet even finding one solution is quite difficult). Adding the 3 color challenge reduces the number of possible solutions to just this one shown here! Made from laser cut acrylic and wood- and now available for the first time in a limited production run.

Nova Plexus Interlocking Puzzle

Precision 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.

Matsuyama's Paradox

Get this and other amazing math puzzles here:

From Etsy: BUY NOW: Missing Square Puzzle

Matsuyama’s Paradox: dissect a large square in to four equal quadrilaterals, rotate and reassemble- to find a small square is missing! Where did the additional area come from? Fun math involved in the design of this puzzle, which illustrates how the concept of area can often challenge our intuitions. Swipe to compare the two assemblies. A precision crafted puzzle by Jeux Efcé game shop. Wikipedia has good details: Missing square puzzle


Four Marble Puzzle

Get this well crafted puzzle from Creative Crafthouse here: 
From Amazon: BUY NOW Crossroads Four Marble Puzzle 
From Etsy: BUY NOW Four Marble Puzzle 

Four Marble Puzzle: physics brain teaser- move all four marbles to their corner locations simultaneously. Each slot slopes down towards the center such that the marbles tend to stay at the center- so, how would one get them to roll outward at the same time? The solution to this puzzle (like others featured here) relies on some fun basic physics principles. Answer below and swipe to reveal solution. A beautiful and well-made puzzle from Creative Crafthouse. 

TrueBalance

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! 

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).


Aristotle's Wheel Paradox 

Get this demonstration puzzle here:

From Etsy: BUY NOW: Aristotle's Wheel

WIkipedia has some details on the Wheel "Paradox"

Aristotle’s Wheel “Paradox”: How does the smaller attached disk travel the same length as the larger one if both disks only make one full rotation? Note the shorter path of the smaller disk, if rolled on its own. This beautifully made demonstration depicts an issue of geometry and motion that perplexed the best minds of humanity for 2000 years. The ancients knew the formula for circumference, and C=2πR for the large disk is clearly greater than C=2πr for the smaller- so how could the smaller disk, rotated once, still travel the distance of the larger one if attached? The great Galileo even offered a solution to the problem in his book Two New Sciences, where he approximated the situation as concentric hexagons and considered the limit as the number of sides increased. So what is the best answer to make sense of this situation?

Two Marble Puzzle

Similar 4 marble version of this puzzle available here: 
From Etsy: BUY NOW Four Marble Puzzle 

From Amazon: BUY NOW: Two Marble Puzzle, or get this set of puzzles

Two Marble Puzzle: physics brain teaser- move both marbles to their top locations on each side simultaneously. The solution to this puzzle relies on some fun basic physics principles- can you figure out which ones? Swipe to reveal solution. Found this well made version of this classic physics puzzle at a gift shop in San Francisco (note Golden Gate Bridge motif).

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! 


In-Feed Google

RPSLK Dice

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. 

Impossible Braid 

Get this nice example of mystery braid here:

From Art of Play: BUY NOW: Impossible Braid Key Fob

Here is a great video on how to make the mystery braid

See other Impossible Objects in my collection. 

Mystery Braid: challenge- how can three strands be braided if both sets of ends are connected? (swipe for reveal) A new addition to my collection of “impossible objects”, this leather key fob is braided from a single piece of leather, constructed by making two parallel slits but not cutting the ends. The solution is well known to those in the field of leatherwork- due to a twist of topology it’s possible to make this braid if the number of left strand over right crossings equals the times the right strand crosses over the left. Four strands braided this way is not mathematically possible, but 3, 5, or any odd number can be done!

 

 


Penrose Aperiodic Rhombs

This set avaiable here:
From : Search NOW Penrose P3 Tiling
Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!) 
Another nice version of Penrose Tilings is available here: 
From Etsy: BUY NOW Penrose Tiles 

Penrose Aperiodic Rhombs: a famous aperiodic tiling with just two shapes- a pair of rhombuses with equal sides, but with the ratio of their areas made to equal the golden ratio. Note that although the starting pattern of 10 tiles is symmetrical, adding any further tiles breaks the symmetry, as highlighted by the path of the double curves. Sir Roger Penrose- who just won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! In this construction, single and double line patterns must align such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.

Square Dissection Puzzles

Get these and other well made disection puzzles here:

From Etsy: BUY NOW: Square Dissection Puzzles

These puzzles are expertly laser cut and sold by GamesEfce. I spray-painted the pieces of mine to better show the shapes and relationships for the video. 

Square Dissection Puzzles: a square can be cut (dissected) into polygons and then reassembled into other regular polygons. Shown here: an equilateral triangle, a pentagon, and a hexagon. These are the record holders for smallest number of pieces needed: triangle (4 pieces by Henry Dudeney 1902), hexagon (5 pieces Paul Busschop 1870s) and pentagon (6 pieces Robert Brodie 1891). Fun fact- It is not known if any of these records are the smallest possible, no mathematical proofs yet exist on this question.

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 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. 

Flippe Puzzle Ball

Get this puzzle ball here:

From Etsy: BUY NOW: Flippe Puzzle Ball

Flippe Ball Puzzle: this ball is a puzzle that explodes and flies apart when spun. The puzzle is made of three identical pieces and a ball bearing which mysteriously locks the pieces together only to release them after a period of spinning. The main challenge is to fully explain why this spontaneous disassembly occurs. Swipe to see a slow motion boomerang loop of it coming apart- and how conservation of momentum has the three equal mass pieces on equally spaced trajectories (120°) with the ball bearing remaining stationary at the center. A product of puzzle master George Bell.

Impossible Jar with Golf Ball

Get this "impossible" jar and other amazing things from this shop:

From Etsy: BUY NOW: Impossible Jar & Golf Ball

Impossible Jar with Golf Ball: a regular off the shelf golf ball somehow trapped within a standard glass jar. Neither the ball nor the jar were cut or glued in the fabrication process. The puzzle aspect is to consider how this object was produced (again, I have some theories- but I do not know the secrets of this artist). This incredible piece was made by craftsman and artist Nathan Nickerson, and comes with the golf tee display stand (a nice touch!)