# The Oldest Puzzle in History?

[Archimedes, looking disappointed for some reason. Image courtesy of Wikipedia.]

Imagine the first puzzle. The very first one. What form would it take? Would it involve words? Numbers? Pictures? Would it be a riddle? A jigsaw? Would there be pieces to move around and place? Would it require scratchings in ink and quill to solve, or marks on a clay tablet?

It’s hard to visualize, isn’t it?

The subject of today’s blog post was probably not the first puzzle, but it’s the oldest puzzle that we can trace back to its origins. And those origins are more than two thousand years in the past.

Fellow puzzlers, allow me to introduce the Ostomachion.

[The puzzle can be found in paper, wood, plastic, and other forms. The original was supposedly made from bone. Image courtesy of Oh So Souvenir.]

The Ostomachion, also known as the Stomachion, the Syntemachion, the Loculus of Archimedes, or Archimedes’ Square, consists of 14 shapes that can be arranged to fill a square.

Created by Archimedes in the 3rd century B.C., the Ostomachion might’ve vanished from history if not for the clever investigative skills of researchers. You see, the Ostomachion was among other writings by Archimedes that were transcribed into a manuscript in 10th-century Constantinople. The manuscript was then scraped clean and reused in the 13th-century as a Christian religious text (becoming a palimpsest in the process), where it remained until at least the 16th century.

[Image courtesy of Harvard. Yes, that Harvard.]

Thankfully, the erasure was incomplete, and in 1840, a Biblical scholar named Constantin von Tischendorf noted the Greek mathematics still visible beneath the prayer text. Another scholar recognized it as the work of Archimedes.

After changing hands multiple times, being sold (most likely illegally), modified by a forger, and then finally allowed to be scanned with UV, infrared, and other spectral bands, revealing the full mathematical text (as well as other works, all of which are now available online).

This palimpsest is the only known copy of both the Ostomachion and another Archimedean work, “The Method of Mechanical Theorems.”

[Shapes to be solved. Image courtesy of Latinata.]

So, all that trouble for a place-the-pieces puzzle? Obviously there’s a bit more at play here.

After a solver has managed to fill the square , they are invited to use the pieces to make a variety of different shapes (similar to tangram puzzles). Players could compete to see who could use all of the pieces to form the different shapes first. It’s believed that this is where the name Ostomachion came from, as it translates to “bone fight” in Greek.

But, naturally, Archimedes didn’t stop there, delving into the mathematics of the puzzle itself, and trying to calculate how many unique solutions there were to the Ostomachion square. How many different ways could you fill the square?

[Cutler’s 17th solution. Image courtesy of MathPuzzle.com.]

That question wouldn’t be answered until 2003, when Bill Cutler — a mathematician with a doctorate in mathematics from Cornell — and some brute-force computing figured out that there were 17,152 solutions.

Seventeen thousand.

But, wait, it’s a square. So, technically, there must be quite a bit of overlap in those solutions, since some of them would be rotations or reflections of other solutions.

So what’s the real answer?

536. 536 distinct solutions. (You can view them all here.)

And it only took 2200 years to find out.

That, my fellow PuzzleNationers, is quite a puzzle.

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# Think outside the house…

[A friendly reminder that not everything is available online.
Stickers (and the story of their creation) can be found here.]

Summer’s almost here, and although we all love puzzles (and we’ve been talking about apps a lot lately), I think it’s safe to admit that puzzles have always been something of an indoor activity. So what’s a parent to do when puzzle-loving kids don’t want to go outside?

Why, take the puzzles outside, of course!

Do your kids enjoy shapes? Why not create some large-scale tangram puzzles for them? All you’d need is a sheet or two of posterboard and a pair of scissors. There are numerous designs online that you could recreate (minus the lines that show how the pieces make each shape) and challenge your young solvers to mimic with their pieces!

You could even cut the posterboard into Tetris pieces and play a game of Tetris where each kid takes a turn placing a piece, trying to leave as few open spaces between pieces as possible. (Though you’d have to be a real magician to make complete lines disappear like in the game!)

Do your kids like trivia? Why not grab a few frisbees, a hula hoop or two, and create a mini-game show!

[Frisbee golf provides the perfect model for an easily improvised puzzle game.]

Different hula hoops could be different categories or difficulty levels (either prop them up or let them sit on the ground), and the kids could show off their athleticism AND their trivia knowledge in one fell swoop! (Replace the frisbees with beanbags or softballs or whatever you like. This is a game meant to be cobbled together from whatever’s on hand.)

And of course, there’s always the ultimate fusion of outdoor adventure and puzzly skills:

Scavenger hunts are great, because you can tailor them to your audience. Do your kids love puzzles? Make the clues as puzzly as possible, incorporating riddles and anagrams and wordplay galore. Do your kids like searching more than puzzling? Be creative in crafting the list of items to find.

Since the dawn of the modern era of mobile phone technology, a new variation on the scavenger hunt has emerged: the photo scavenger hunt. Instead of finding numerous items and bringing them back to a predetermined spot, you take pictures of various items (or provide photographic proof that you’ve completed certain activities or accomplished certain tasks) and bring your phone back as evidence.

Some companies, like our friends at The Great Urban Race, offer city-specific scavenger hunts for adults, replete with puzzles, physical challenges, and all kinds of outdoor fun. Their website is a treasure trove of ideas for your own adventures.

Actually, you know what? That sounds great. Forget the kids, I’m gonna go recruit some people and go scavenging!

Thanks for visiting PuzzleNation Blog today! You can share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and be sure to check out the growing library of PuzzleNation apps and games!

# Tile style puzzling!

Tile puzzles and tile games have been with us for centuries, but I daresay they’ve never been as prominent in our game/puzzle culture as they are these days.

Chinese Dominoes, which are slightly longer than the regular ones pictured above (not to mention black with white pips), can be traced back to writings of the Song Dynasty, nearly a thousand years ago. Dominoes as we know them first appeared in Italy during the 1800s, and some historians theorize they were brought to Europe from China by traveling missionaries.

The most common form of playing dominoes — building long trains or layouts and trying to empty your hand of tiles before your opponent does — also forms the core gameplay of other tile-based games, like the colorful Qwirkle, a game that combines dominoes and Uno by encouraging you to create runs of the same shape or color.

A tile game with similarly murky origins is Mahjong, the Chinese tile game that plays more like a card game than a domino game. (Mahjong is commonly compared to Rummy for that very reason.)

Mahjong has been around for centuries, but there are several different origin stories for the game, one tracing back to the Ming Dynasty (1368-1644), another to the days of Confucius (500 BC). The gameplay itself is about matching tiles (called melds) to build winning hands.

Rummikub, another tile game (but with numbers instead of characters on the tiles) also resembles card games in its gameplay, and anyone who has played Texas Rummy or Go Fish will instantly recognize the gameplay of building runs (1, 2, 3, 4 of the same color, for instance) and sets (three 1s of different colors, for instance).

All of these games employ pattern matching and chain thinking skills that are right in the puzzler’s wheelhouse, but some more modern tile games and puzzles challenge solvers in different ways.

The game Carcassonne is a world-building game wherein players add tiles to an ever-growing landscape, connecting roads and cities while placing followers on the map in order to gain points. Here, the tiles form just one part of a grander strategic puzzle, one encouraging deeper plotting and planning than some other tile games.

The Settlers of Catan also involves tile placement, but as more of a game starter, not as an integral part of the gameplay. Both Fluxx: The Board Game and The Stars Are Right employ tile shifting as a terrific puzzly wrinkle to their gameplay.

Our friends at Penny/Dell Puzzles have a puzzle combining crosswords and tiles, Brick by Brick, which encourages the solver to place the “bricks” on the grid and fill in the answers.

And, of course, I’d be remiss if I didn’t mention the most popular electronic tile game in modern memory, Tetris.

Tetris — which turns 30 this year! — requires quick thinking, good spatial recognition, and an ability to plan ahead (especially for those elusive four-block pieces that can eliminate four rows at once!). There are plenty of puzzles that employ similar tiles — Blokus, tangrams, and pentominoes come to mind — but none that have engendered the loyalty of Tetris.

Last but not least, there are the sliding-tile puzzles. These puzzles take all the challenge of tile placement games like Dominoes and add a further complication: the tiles are locked into a frame, so you can only move one tile at a time.

Frequently called the Fifteen Puzzle because the goal is to shift all 15 numbered tiles until they read out in ascending order, sliding-tile puzzles are chain solving at its best. Whether you’re building a pattern or forming a picture (or even helping a car escape a traffic jam, as in ThinkFun’s Rush Hour sliding-tile game), you’re participating in a long history of tile-based puzzling that has spanned the centuries.

Heck, even the Rubik’s Cube is really a sliding-tile game played along six sides at once!

[Be sure to tune in on Thursday, when I explore tile-based word games like Scrabble!]

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# Celebrating a true elder statesman of puzzles

Yesterday was Martin Gardner’s birthday. (And unfortunately, I wasn’t feeling well, so I apologize for not getting this post up in a more timely manner.)

If you don’t know Martin Gardner, you absolutely should.

For twenty-five years, he penned a column in Scientific American called Mathematical Games, adding a marvelous sense of puzzly spirit and whimsy to the field of mathematics, exploring everything from the works of M.C. Escher to visual puzzles like the mobius strip and tangrams.

His affection for magic, puzzles, and mathematics was infectious, and events known as Gatherings 4 Gardner began springing up. After his passing on May 22, 2010, his legacy now lives on thanks to an annual global event known as the Martin Gardner Celebration of Mind.

Magic tricks, puzzles, recreational math problems, and stories about Martin are shared by admirers and devotees, all in the hopes of maintaining and spreading the wonderful spirit of playful mathematical experimentation that Gardner embodied so brilliantly.

So today, we here at PuzzleNation invite our fellow puzzle fiends and math lovers to join us in celebrating not only Martin’s life and love of all things mathy and puzzly, but the marvelous tradition of sharing those interests with others.

And in the spirit of sharing similar puzzle joy, I proudly give you our own little contribution… the mobius bagel.

[For a complete bibliography and breakdown of the fifteen printings of Gardner’s Mathematical Games columns, click here. To check out some of his many delightful columns, click here. And to solve a number of Martin’s most popular puzzles and brain teasers, click this link provided by our friends at ThinkFun.]

Thanks for visiting the PuzzleNation blog today! You can like us on Facebook, follow us on Twitter, cruise our boards on Pinterest, check out our Classic Word Search iBook (recently featured by Apple in the Made for iBooks category!), play our games at PuzzleNation.com, or contact us here at the blog!