Can you assign a unique number to all the keyring chains below and sort them accordingly?

enter image description here

After you finished, can you think of arrangements that give some other numbers, different from the 15 cases above? The rings have to stay connected.

  • 2
    $\begingroup$ Looks like how they made the olympics symbol :P $\endgroup$ Jan 19, 2017 at 20:56
  • $\begingroup$ Safe to say that color is optional? I don't (yet?) notice any duplicate topologies. $\endgroup$
    – humn
    Jan 19, 2017 at 21:12
  • 1
    $\begingroup$ @humn, color is optional, yes $\endgroup$
    – Yuriy S
    Jan 19, 2017 at 21:12
  • $\begingroup$ boboquack's answer shows how exquisitely efficient the few clues are. $\endgroup$
    – humn
    Jan 20, 2017 at 4:15

1 Answer 1


The values are:



For each keyring, you take the number of intersecting keyrings, then multiply all those numbers together to get the final result.

New value:

New value

Sorted (Quite grainy, so refer to above images):

Sorted values


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