The word “puzzle” is rare in English. Marcel DanesiThe University of Toronto professor of semiotics says that these words “have no equivalent in other languages,” and encompass everything from riddles and logical conundrums to mathematical problems and optical illusions.
That might seem reasonable: this set of brainteasers clearly doesn’t have much in common. But at the most basic level, all puzzles (jigsaw puzzles, crossword puzzles, detective stories) relate directly to what Danesi calls a “question and answer” structure. Puzzle Instinct.
“When we don’t get an answer, we feel a kind of emptiness,” he says, “and then when it’s finally filled, we feel an intellectual catharsis.” In other words, we’re hardwired to handle cognitive challenges.
The origins of this problem-solving urge are unclear, and it would be difficult to pinpoint the exact time when our ancestors started solving puzzles. But we do know that puzzles began appearing all over the world as soon as historical records began to appear. Here are some of the most famous ones.
1. Ishango Bones
In 1950, Belgian geologist Jean de Heinzelin discovered the lake on the shores of Lake Edward in what is now the Democratic Republic of the Congo. The oldest puzzleAt first glance, it looks ordinary – like a bone with random markings or some junk from the 11,000-year-old fishing village of Ishango – but the closer you look, the more meaning the inscriptions reveal.
These are divided into three columns, each unified by what appears to be a mathematical theme. One revolves around the idea of doubling numbers: after the three lines come together, there’s a column of 6s, 4s, 8s, 10s, and two sets of 5s. The other column revolves around multiples of 10, a key core of the modern decimal system: 11, 21, 19, and 9. The third column lists four numbers – 11, 13, 17, and 19 – which, incredibly, are all prime.
Coincidence? De Heinzelin didn’t think so. In his view, the marks represent “a kind of arithmetic game” that would have been surprisingly advanced for the Paleolithic period. If he was right, mathematics writer Dominic Olivastro wrote in his book: Ancient puzzles“This is certainly the oldest puzzle.”
2. The Mystery of the Sphinx
Whatever the true nature of the Ishango bone, the true ancestor of all puzzles Mystery of the Sphinxthe best known is Oedipus the KingA tragedy by the Greek poet Sophocles, in this story the Sphinx is a merciless hybrid creature with the head of a woman and the body of a lion who stands guard at the gates of Thebes, posing riddles questions to all who attempt to enter the city.
“What has four legs in the morning, two legs in the afternoon, and three legs in the evening?”
The monster quickly devours anyone who answers incorrectly. However, only Oedipus understands the correct answer: a human being who crawls on all fours as a baby, walks on two legs as an adult, and uses a walking stick in old age. This riddle is actually an allegory for the journey of life, and will be familiar to modern readers.
“We never think of metaphors as a mystery, because we’re used to it,” Danesi says, but it’s easy to imagine Greek theater audiences scratching their heads for answers.
3. Stomachion
You’re probably familiar with tangram, the anatomical puzzle of seven polygons connected to form a square that can be arranged into a variety of shapes, from birds to houses to sailing ships. But long before this popular modern game was invented (probably in China in the late 1700s), it had a Greek precursor.
The Greek mathematician Archimedes Stomachion (also known as Roculus) is a further evolution of Tangram, with twice the number of geometric shapes that can be rearranged and reconfigured to create more complex shapes, like intricate gladiators, warships, or elephants.
By creating meaningful pictures from abstract shapes, the game acts as a “blueprint for Lego, jigsaw puzzles and tangrams,” Danesi said.
In some versions, the goal may have been to connect the shapes together to form a square, a process similar to a jigsaw puzzle. In 2003, mathematician Bill Cutler revealed that there are 536 unique ways to form a square, excluding solutions that are identical when rotated or flipped.
4. Crossing the River
In the Middle Ages, puzzles began to take root as a form of entertainment. Around 800, the English cleric Alcuin of York Aquendos Hubenes’s proposal (“Problems to Sharpen the Young”) is what Danesi calls “the first great puzzle book.” It contains about 50 problems, the most famous of which is the river crossing puzzle, which spawned a genre.
Here’s the classic version: You have to cross a river with a wolf, a goat, and a cabbage, but your boat is only big enough to carry you and one other load at a time. You want to leave all your cargo intact on the other side of the river, so you can’t just leave the wolf and the goat, or just the goat and the cabbage. How do you proceed? (Hint: Which combination ends without someone/something getting swallowed?)
Based on one of Alcuin’s letters to Charlemagne, Olivastro suggests that the scholar may have created the puzzle to entertain the first Holy Roman Emperor. If you think of Wordle as an essential after-work pastime, imagine trying to relieve stress while working to conquer all of Europe.
5. The Knight’s Journey
Around the same time, chess (or rather, an early form of chess) Chaturanga) was gaining popularity in India. Nowadays, chess has become a staple for serious players, and it was back then too. One move in particular stands out: the knight tour, in which the knight travels to all 64 squares on the board, never landing on the same square more than twice.
of The quickest solution These are the words of Rudrata, the 9th century Kashmiri poet. KavyalankaraIn his Sanskrit work on poetics, he uses The Knight’s Course (which only covers half the board) to create a fascinating and oddly shaped poem: each of the 32 syllables corresponds to a square, and the order remains the same whether you read it from left to right or along the Knight’s Course.
If you think these are just dusty old puzzles with no relevance, think again: In the 2010 World Chess Championship match between defending champion Viswanathan Anand and Veselin Topalov, Anand made 13 consecutive knight moves, leading online commentators to joke that he was trying to solve the Knight Tournament.
6. Rabbit Puzzle
Italian mathematician Leonardo de Fibonacci is widely known for the number sequence of the same name, in which each number is the sum of the two previous numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. The Fibonacci sequence became famous when biologists discovered examples of it. throughout nature — The spiral patterns on pine cones, flower petals, and nautilus shells all reflect that formula.
What’s less known is that he stumbled upon this sequence by chance after devising a completely arbitrary puzzle about rabbit reproduction: It starts with a pair of male and female rabbits. Every month, each pair gives birth to a new pair, which start laying in their second month of life. How many rabbits will there be by the end of the year?
Fibonacci could not have known how amazing the answer would be: as the numbers increase, their ratios approach the golden ratio (approximately 1.618). Leonardo da Vinci and other artists used the golden ratio as a model for ideal proportions in their work. This abstract mathematical concept appears again and again in organic life as well as aesthetics. In words Mathematician Ian Stewart says, “A simple puzzle could reveal hidden depths of the universe.”
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Cody Cottier is a contributing writer at Discover who loves exploring big questions about the universe and Earth, the nature of consciousness, the ethical implications of science, and more. He holds a BA in Journalism and Media Production from Washington State University.
