Riddle of the Sphinx

When is a riddle like a passcode? That’s not a riddle by the way. The Sphinx guarded the gate to the city of Thebes and required travellers to answer a riddle before gaining access to the city.

Riddles are a bit like passcodes. They typically present as permutations, combination of elements, albeit for small numbers, usually around the 2, 3 or 4, or at least a subset of possible combinations.

What is the creature that walks on four legs in the morning, two legs at noon and three in the evening? That’s the Riddle of the Sphinx. It draws on permutations of morning, noon and evening and the number sequence 2, 3 and 4.

By most accounts, the key to resolving the riddle is to appreciate that morning, noon and evening could apply to the early middle and final stages of life, and that the term “legs” could apply to arms and walking sticks as well. So the resolution to the riddle of the Sphinx presented to the traveller is “a man.”

sphinx - 2

Jokes and humour

A riddle is a kind of joke, and falls within the purview of humour. Theorists of humour agree there are three elements to a joke: there has to be incongruity, a resolution, and it’s important that there’s some indication there’s a joke in play. For the authors of The Psychology of Humor

“humor involves an idea, image, text, or event that is in some sense incongruous, odd, unusual, unexpected, surprising, or out-of-the-ordinary. In addition, the humor stimulus must be accompanied by cues that signal us to appraise the stimulus in a playful, nonserious, nonliteral frame of mind in which people temporarily abandon rules of logic and expectations of common sense and congruity” (4).

Combinations and permutations provide signals that we are dealing with a non-serious joke context. The rhythm, repetitions and cadences of the riddle alert us to the fact that we are dealing with just that — a riddle.

The format of the Sphinx riddle involves a subset of all possible combinations of times of the day (morning, noon, evening) and numbers of legs (2, 3, 4). There are 9 possible combinations of 2 sets of 3 elements from which the riddle provides just 3 combinations. Constraining the permutations to 3 or 4 makes sense. Beyond that we lose the thread of the narrative — and the joke. See blog post: Triadomania.

Permutations increase the chances of hitting on an incongruity. After all, it’s the tactic of the surrealists to rearrange and juxtapose familiar elements in unfamiliar (incongruous) ways. (See post: Data waste.) So the permuted riddle format also fulfils the criterion of incongruity.

The permutations selected for the Sphinx riddle works. For example, I’m hard pressed to find a simple resolution to an “alternative” riddle (I just made up): What has two legs at noon, one in the evening and three in the morning.

Up a chimney

What goes up the chimney down but cannot go down the chimney up? That’s also a riddle that begins with permutations — of “up” and “down.” At first glance the question appears contradictory, paradoxical, nonsensical and therefore incongruous. How is it resolved?

The solution requires a frame shift to appreciate that “up” and “down” have different meanings depending on context. An umbrella is “up” if it is open, but it can also go up a chimney if you put it up there, and that’s very difficult to do if the umbrella is up (i.e. open).

As kids I recall we thought you could probably force an upright umbrella up a chimney if it is open as the direction of movement could force the spokes into the closed position (if they are flexible enough). To push the umbrella down a chimney while up would really wreck the umbrella — unless it was upside down! What can go up a chimney down, down a chimney down and up a chimney up but cannot go down a chimney up?

Perhaps there’s a meta-riddle in play that appeals to the unfettered mind of the child. To the child it’s the combinatorial, repetitive and rhythmical aspect of the riddle space that provides the initial appeal — even before the child appreciates the mechanics of the circumstances, and the ambiguity and its resolution that provide the joke.

Locks and riddles

I’m here investigating riddles because they involve permutations and combinations. Locks and puzzles depend on permutations. Riddles are a kind of puzzle or key. After all, the Sphinx required an answer to the riddle before the traveller could enter the city. To enter the city you had to answer the riddle correctly — or die trying.

The challenge was not to establish a correct combination, but to provide a key, the answer, that ensured that the combination made sense, and resolved the incongruity.

By one theory, the transition from the incongruity in the statement of the riddle to a resolution constitutes an aha moment. The transition from confusion to clarity provides a moment of enlightenment, satisfaction, pleasure, even delight. See post on aha moments.

The Sphinx riddle presents something odd, incongruous or contradictory — something that grows an extra leg through the day, or something that is up and down at the same time. The answer, or resolution, is to identify this creature or object as something simple, prosaic or ordinary after all — a man or an umbrella.

The riddle presents something extraordinary, impossible or monstrous, like the Sphinx him/herself — a lion with the face of a human being — and transitions to something reassuringly ordinary.

Cities and clarity

Buildings and cities involve combinations of elements, spaces, rooms, furniture, functions, etc. In this respect they form the basis of a riddle, or at least a puzzle.

A floor plan follows the format of a kind of puzzle, as a designer creates it, and as visitors move through it. The experience of the city also presents as a riddle, at least for the first time visitor. See post Everything is code.

Movement through a city can have the character of a riddle — moments of confusion followed by moments of clarity. Confusing, disorienting or jumbled spaces transition to open, clear, ordered places. Permutations of elements in the visual field that present contradictions transition to an overview that shows that the whole place makes sense after all.

Think of moving through the tangle of streets in an old medieval city, and the need felt by the fit and able to climb to the top of a tower to see how the city looks from above, and to make sense of the jumble of relationships experienced at ground level, and discover that the cathedral is around the corner from the town hall, which is adjacent to the cafe you just visited. There’s pleasure in that, the contrast and the transition — like solving a riddle.


  • Martin, Rod A., and Thomas Ford, A. 2018. The Psychology of Humor: An Integrative Approach. Cambridge, MA: Academic Press
  • Shultz, Thomas R. 1974. Development of the Appreciation of Riddles. Child Development, (45) 1, 100-105.


  • “If I were to compare Great Britain to a sphinx, the sphinx would be an open book by comparison” —European Commission President Jean-Claude Juncker. (Politico)
  • The resolution to the Sphinx riddle is of course that humans crawl on all fours in infancy, then 2 legs as adults, then with a walking stick in old age. One variant of the riddle has the human with no legs at night. That’s the human after death.
  • First picture shows the Sphinx at Giza, Egypt, December 2006. The second is Dubrovnic, Croatia, December 2016.
  • Dr Seuss stories are a good source of permutations that are on the verge of a riddle: “Think left and think right and think low and think high. Oh, the things you can think up if only you try!” (Dr Seuss Quotes).
  • The article by Shultz on riddles and children (above) doesn’t refer to the issue of permutations in establishing the riddle context, nor to the allure of permutations for children or adults. But he does identify incongruity as providing the key to the way a riddle functions.


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