[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.
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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