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In ancient Greek geometry, the Ostomachion, also known as loculus Archimedius () or syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic language version and a copy, the Archimedes Palimpsest, of the original ancient Greek text made in Byzantine Empire times.Darling, David (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley and Sons, p. 188.
The word Ostomachion (Ὀστομάχιον) ὀστομάχιον, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library comes . ὀστέον, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library μάχη, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library The manuscripts refer to the word as " Stomachion", an apparent corruption of the original Greek. Ausonius gives us the correct name "Ostomachion" (quod Graeci ostomachion vocavere, "which the Greeks called ostomachion").
The Ostomachion which he describes was a puzzle similar to and was played perhaps by several persons with pieces made of bone.Ausonii Cento nuptialis in Monumenta Germaniae Historica, auctores antiquissimi, vol. 5, part 2: D. Magni Ausonii opuscola, Berolini apud Weidmannos, 1883, pagg. 140-41 . It is not known which is older, Archimedes' geometrical investigation of the figure, or the game. Victorinus,Ars grammatica, III, 1 in Grammatici latini, Lipsiae in aedibus R. G. Teubneri, 1857, vol. 6, part 1, pagg. 100-01. Caesius BassusDe metris, 9 in Grammatici latini cit., pagg. 271-72, Ennodius Carmen CCCXL (2, 133) in Monumenta Germaniae Historica, auctores antiquissimi, vol. 7, Magni Felicis Ennodi opera, Berolini apud Weidmannos, 1885, pag. 249 and Lucretius De rerum natura, II, 776-787 cited in have also discussed the game.
The number of different ways to arrange the parts of the Stomachions within a square were determined to be 17,152 by Fan Chung, Persi Diaconis, Susan P. Holmes, and Ronald Graham, and confirmed by a computer search by William H. Cutler. However, this count has been disputed because surviving images of the puzzle show it in a rectangle, not a square, and rotations or reflections of pieces may not have been allowed.
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