Introducing Archimedes' Ostomachion

The Ostomachion or Stomachion ("ὀστοῦν"[ostoun] + "μάχη" [mache], that is "bones" + "battle" which means the battle of the bones) is documented in the famous Archimedes Palimpsest. It is perhaps the world's first logic game, the original puzzle!

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A square is divided into 14 polygons in an ingenious geometric way (the ratio of the square's area to the area of each of these polygons is a rational number).

Archimedes seeks the number of ways in which these polygons can be rearranged to form the square again. Additionally, he investigates the types of polygons that can be created by rearranging the 14 pieces, as well as various figures that can be formed from them (a different version is the well-known Tangram, where 7 polygons create various figures).

Geometry of Ostomachion

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                      In a complex and ingenious way we divide an initial square into 14 polygons as shown in the figure.

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These 14 polygons have the characteristic that the ratio of the areas of these polygons to the area of the initial square is a rational number.! Calculating the areas of the polygons, in relation to the initial square, requires basic knowledge of Euclidean Geometry and requires delicate manipulations ... so it is a very nice challenge for Geometry lovers.

...for more information: Geometry(Book 3), Chapter 2, pages 154-164 book3

The first combinatorics problem

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      Do you think you can figure out one way to re-form the original square, if the polygons are taken out of it?

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Archimedes' search for finding the ways in which the square is formed after rearranging the polygons constitutes perhaps the world's first combinatorics problem: "how many different arrangements exist?"

For its solution, in addition to the typical mathematical knowledge required for calculating the total number of arrangements, it was also necessary to invent the method by which these rearrangements could be done!

The total count was performed using computers, but the invention of the arrangements (the ways to put the pieces together) was done with "paper and pencil" or, as we say, with "ruler and compass."

From the preceding analysis, the result emerged: the total number of ways the original square can be re-formed is 17,152. However, if we take into account the equality (sameness) of some polygons and the symmetry of some formations, the completely unique ways are 536.

Let's play Ostomachion, the first logic game in the world!!

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Press start, and you will see the polygyny - pieces (Bones) outside the square!!! You are invited to find one of the 17152 different ways to reposition them inside the square frame, Can you find one???

Classic game	game description -instructions	video
	Play what is likely the world’s first logic game, a puzzle .. Play the Archimedes’ Ostomachion ! When you press Start, the pieces — polygons (Osta) of the Ostomachion — are rearranged and move outside the square frame. Your task is to place the Osta back into their original arrangement. Helpful tools are available to make the experience more enjoyable: view the classic arrangement frame, take a photo, or use an image from your device to recreate the original Ostomachion.

free Style game	game description -instructions	video
	You are invited to reposition the pieces - polygons (Osta) of Ostomachion in the square frame.Αttention : here there is no initial arrangement . There are 17152 different ways that the original square can be re-formed . Although the challenge may seem easy at first, you will soon discover how difficult it is to find even one !!!! It is certainly a very challenging game, but helpful tools are provided to make your search more enjoyable and creative. You can press the magnet button to select one of the available layouts or to unlock a new one. The selected layout will function as the initial layout, allowing you to play the Classic game with a different arrangement. If you press the unMagnet button you will return to the Freestyle game, without an initial layout. This will help you understand the logic behind creating different layouts and allow you to design a new one yourself — one of the 17,152 possible arrangements. Here you can rotate each polygon (“Ostο”) of the Ostomachion : tap for clockwise rotation, double-tap for anticlockwise rotation, or long-press ) to reverse it. Feel free to add your own photo or choose any color. Cubism is already visible— share the light with your rearranged pieces to your loved ones.

Follow the challenge of Archimedes.....

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Using all 14 polygonal pieces (Osta), create a figure as best as you can. Challenge a friend , just as Archimedes suggested, to see who can do it better. ....
The method is similar to the well-known tangram, but here the challenge is greater and the possibilities are endless —  let your imagination run free.

Figures	game description -instructions	video
	This is perhaps the most creative game of the Ostomachion. Archimedes challenges you to test your imagination: create a figure using all the the pieces — polygons (Osta), or compete with a friend to see who can make it better.

Picasso	game description -instructions	video
	Here, imagination and creativity have no limits. Create anything you can imagine! Apply Cubism and, like a modern Picasso, design what you desire. Don’t forget to share your creation with your loved ones… and beyond!

Control button

Buttons	video	video
Start	Press this button and the pieces — polygons (Osta) from the Ostomachion will come out and be moved outside the target ....
Reset	Start a new game with the original image of Ostomachion
Restart	Put the pieces — polygons (Osta) back into the square frame and play again whithout losing your personal configuration
Hint	Press this button and the layout of your current game will appear in the square frame.
Magnet	This button appears when you play the Freestyle game . It allows you to select one of the available layouts or unlock a new one, so you can play the Classic game with a different arrangement..
UnMagnet	Press this button and you will return to the Freestyle game, without an initial layout.

Personalize the Ostomachion

Buttons	video	video
Gallery	By pressing this button, you can create an Ostomachion using a photo from your collection.
Camera	Take a selfie, or any other photo, and make the Ostomachion your personal story.
Color Picker	Choose a color from the color picker, and the Ostomachion will appear in that color.
Share	Share a figure, your photo, or anything else you create with Ostomachion.
Save	Save the content you have created to your device.