What's the oldest recorded puzzle?

Question

So this starts out as a pretty simple question: what's the oldest recorded puzzle?

I'm aware that we could get into "what's the definition of a puzzle" here, and I don't want to get sidetracked by that, so I'm expanding the question a bit to cover:

• What are some interesting puzzles from ancient civilisations (Greek, Roman, Egyptian, Babylonian, Sumerian, Persian, Aztec, Inca, etc)?

• What are the oldest known puzzles of particular types? (e.g. physical puzzles which survive as artifacts, wordplay, image puzzles)

Answer 1

The best answer I can think of in a serious vein is the Sphinx's riddle, solved by Oedipus in ancient Greece way back in the mists of time. This is surely the oldest riddle if not the oldest puzzle. Here's the story from Apollodorus 3.5.8:

Laius was buried by Damasistratus, king of Plataea, and Creon, son of Menoeceus, succeeded to the kingdom. In his reign a heavy calamity befell Thebes.

For Hera sent the Sphinx, whose mother was Echidna and her father Typhon; and she had the face of a woman, the breast and feet and tail of a lion, and the wings of a bird.

And having learned a riddle from the Muses, she sat on Mount Phicium, and propounded it to the Thebans.

And the riddle was this:— What is that which has one voice and yet becomes four-footed and two-footed and three-footed?

Now the Thebans were in possession of an oracle which declared that they should be rid of the Sphinx whenever they had read her riddle; so they often met and discussed the answer, and when they could not find it the Sphinx used to snatch away one of them and gobble him up.

When many had perished, and last of all Creon's son Haemon, Creon made proclamation that to him who should read the riddle he would give both the kingdom and the wife of Laius.

On hearing that, Oedipus found the solution, declaring that the riddle of the Sphinx referred to man; for as a babe he is four-footed, going on four limbs, as an adult he is two-footed, and as an old man he gets besides a third support in a staff.

So the Sphinx threw herself from the citadel, and Oedipus both succeeded to the kingdom and unwittingly married his mother, and begat sons by her, Polynices and Eteocles, and daughters, Ismene and Antigone.3 But some say the children were borne to him by Eurygania, daughter of Hyperphas.

Some more flippant answers:

• "What is the meaning of life?"

• "Why?"

(In true AE-style I've even included a link to a Youtube video!)

Answer 2

What a nice question! Of course, there is no perfectly correct answer, as our historical knowledge is far too incomplete. I list some puzzles from before 1000 BC.

• 2700 BC: Carved stone balls. They show all regular polyhedra and the cubo-octahedron. There purpose is unclear, but they are usually listed as the starting point of recreational mathematics.

• 2300 BC: Tablets of Nippur. List divisors of $60^4$ in geometric progressions. Most likely "serious" research, and not puzzle-type entertainment.

• 1700 BC: Phoenician puzzle jugs in Cyprus. Puzzle jugs are the oldest known mechanical puzzles. Several examples can be seen in the Metropolitan Museum of Art in New York. Puzzle jugs came back into fashion in ancient Greece (http://en.wikipedia.org/wiki/Pythagorean_cup), and much later in the 18th and 19th century, in France, Germany, England.

• 1650 BC: The Rhind Papyrus. Problem 79 is a kind of St. Ives puzzle. Problem 40 is a fair division puzzle.

• 1400 BC: Morris boards in Kurna (Egypt). wikiipedia

All the listed dates are of course estimates. Magic squares were introduced in China perhaps around the same time, but the earliest sources (available nowadays) that mention them are from 700 BC.

Answer 3

In early mathematical puzzles, the "inventory problem" is addressed in the Egyptian Rhind papyrus, and may go back to 2650 BC / BCE.

Answer 4

Archimedes' cattle problem is ascribed to Archimedes; if this is true (which there is some debate about), then it goes back to the third century BCE. It reads:

Compute, O friend, the number of the cattle of the sun which once grazed upon the plains of Sicily, divided according to color into four herds, one milk-white, one black, one dappled and one yellow. The number of bulls is greater than the number of cows, and the relations between them are as follows:

White bulls =$\left(\frac{1}{2} + \frac{1}{3}\right)$ black bulls + yellow bulls,

Black bulls =$\left(\frac{1}{4} + \frac{1}{5}\right)$ dappled bulls + yellow bulls,

Dappled bulls =$\left(\frac{1}{6} + \frac{1}{7}\right)$ white bulls + yellow bulls,

White cows =$\left(\frac{1}{3} + \frac{1}{4}\right)$ black herd,

Black cows =$\left(\frac{1}{4} + \frac{1}{5}\right)$ dappled herd,

Dappled cows =$\left(\frac{1}{5} + \frac{1}{6}\right)$ yellow herd,

Yellow cows =$\left(\frac{1}{6} + \frac{1}{7}\right)$ white herd.

If thou canst give, O friend, the number of each kind of bulls and cows, thou art no novice in numbers, yet can not be regarded as of high skill. Consider, however, the following additional relations between the bulls of the sun:

White bulls + black bulls = a square number,

Dappled bulls + yellow bulls = a triangular number.

If thou hast computed these also, O friend, and found the total number of cattle, then exult as a conqueror, for thou hast proved thyself most skilled in numbers.

The problem was rediscovered in the late 18th century, but the actual solution wasn't found until 1880. Notably, the actual solution is incredibly large:

Approximately $7.76 \times 10^{206544}$ cattle.

This raises doubts about whether Archimedes or his contemporaries actually knew the solution to this problem (though he did think about very large numbers in his time, so who knows?)

Answer 5

I’m astonished that there is an answer here that mentions Archimedes, and yet nobody has mentioned the Eureka! puzzle, which started as

How do you measure the purity of metal (that is claimed to be gold) using 200 BC technology?

This is trivially solved as

weigh it, measure its volume, and divide.  If you get a ratio other than the density of gold (which was well known), then it’s not pure gold.  (If you stipulate that it’s a mixture of silver and gold, then it’s straightforward to compute the proportion of each.)

but this gave rise to a subordinate puzzle,

How do you precisely measure the volume of an object of irregular shape?

Archimedes famously realized the answer while bathing:

immerse the object in water, and measure the volume of water that is displaced.

Wikipedia says that Archimedes lived c. 287 BC – c. 212 BC, but it doesn’t give an exact date of this incident.