5
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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.

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  • 2
    $\begingroup$ Looks like how they made the olympics symbol :P $\endgroup$ – Beastly Gerbil Jan 19 '17 at 20:56
  • $\begingroup$ Safe to say that color is optional? I don't (yet?) notice any duplicate topologies. $\endgroup$ – humn Jan 19 '17 at 21:12
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    $\begingroup$ @humn, color is optional, yes $\endgroup$ – Yuriy S Jan 19 '17 at 21:12
  • $\begingroup$ boboquack's answer shows how exquisitely efficient the few clues are. $\endgroup$ – humn Jan 20 '17 at 4:15
4
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The values are:

Values

Because:

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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