Text-only page from part i of Planetarium

The text-only versions of pages in Planetarium are provided to make it easy for you to print a puzzle, without having problems with background colour or graphics. Note that there may be essential parts of the puzzle in illustrations and other parts of Planetarium which are not included on this page.

An Ouroborus in a jar on the shelf:

Ouroboruses make strange pets. The girl has three, but she keeps them, like this one, in separate jars.

On first inspection, in their jars, or aquariums, or ouroboriums, they appear to be simply domesticated serpents, writhing as they do suspended in the ether. But of course, there’s more to mythological creatures, even domesticated varieties, than meets the eye. Know this about the ouroborus: when one chooses to bite its own tail — a choice which sooner or later every one of its kind is destined to make — it cannot release it. It will spend the rest of its existence as a never-ending loop. It might twist and writhe and flatten and flex, but it is forever hooped.

Because of this, there is a terrible risk of two — or more — ouroboruses becoming inextricably linked, should one accidentally bite its own tail whilst passed through the closed hoop of another. To prevent themselves unintentionally spending eternity connected with each other in this way, from their first days as hatchlings, young ouroboruses are taught this important difference:

The girl keeps her three ouroboruses in three separate jars, for fear that at least one of them is foolish, and they end up inseparably connected, all three together. One of the three has already bitten its own tail, and the remaining two, whenever she asks, insist that all three are wise. In which case, is there any risk if she puts them together?

From time to time, the girl has tried to reason it out: is it possible for three wise ouroboruses (one already hooped) to become inseparably entangled?

The answer to the Tangling Ouroborus problem is the either-or key for part x
  • yes, possible
  • no, not possible

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