The bathhouse you work at is being visited by some of the primordial beings from the pools of chaos. You have been tasked with finding out which pools they came from, so that the proper form of chaos can be made for them.

Unfortunately, the primordial ones can't speak, so you can't ask where they came from. It is also dark, making them hard to see. However, you can make out a few features of the limbs. You know that the primordial ones are symmetrical, with paired limbs divided into 4 types: legs to walk on earth, fins to steer through water, wings to fly through the air, and arms to handle fire. You also know that the number of limbs is linked to the proportion of elements in their chaos, and therefore that all primordial ones have at least one of each limb type. You also know that the position of the limbs is defined by a few rules: Legs must be in the outer thirds of the body, Fins are only found as a run at the end of the body, wings must be in the inner third of the body, and arms are only found as a run at the front of the body.

Observing the primordial ones, you see it has 30 limbs in total, with one discernible feature: a fin with 3 limbs behind. They also seem to like fire and air equally, whereas they dislike water and earth, to different degrees. What is their preferred proportions for their chaos?

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    $\begingroup$ I am not sure I can visualise what is meant by inner and outer thirds and what shape the body is supposed to be - are these "thirds" between ends? $\endgroup$ Commented Aug 3, 2021 at 15:54
  • $\begingroup$ @htmlcoderexe The limbs are in series along the body, like a centipede. The thirds are based around the limbs $\endgroup$ Commented Aug 3, 2021 at 16:04
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    $\begingroup$ So all the restrictions are around the same axis and it simply says that limb types have to go in a specific fixed order of arms, wings, legs, fins? $\endgroup$ Commented Aug 3, 2021 at 16:11
  • $\begingroup$ @htmlcoderexe Yes, but the legs could be in either the first or last third, not just the last one $\endgroup$ Commented Aug 3, 2021 at 16:14
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    $\begingroup$ now I understand the meaning of outer and inner. Are you observing the creature from its front, so the limbs behind the one fin that you can see can only be assumed to be more fins because they are at the end? $\endgroup$ Commented Aug 3, 2021 at 16:16

2 Answers 2


One possible answer (from front to back):

  • 10 arms (5 on each side)
  • 10 wings (5 on each side)
  • 2 legs (1 on each side)
  • 8 fins (4 on each side)

As far as I can tell, this meets the requirements:

  1. Arms are all in a line at the beginning
  2. Wings are all in the middle third
  3. Legs are all in the outer two thirds (in this case, they're all in the back third, but that technically follows the rules)
  4. Fins are all in a line at the end
  5. Numbers of arms and wings are equal (for fire and air)
  6. Number of legs and fins (earth/water) are not equal, and are less than fire and air.
  7. He sees one fin with three behind it, leading me to believe it's 8 fins total (i.e. 4 on each side).
  • $\begingroup$ The question says 30 limbs, not 30 pairs of limbs $\endgroup$ Commented Aug 3, 2021 at 16:55
  • $\begingroup$ Are pairs of limbs required to be the same? I.e. in the back, are there 8 fins (4 on each side)? or 4 fins, and then opposite them are legs? $\endgroup$
    – phroureo
    Commented Aug 3, 2021 at 16:58
  • $\begingroup$ The pairs are symmetrical, and both sides are the same $\endgroup$ Commented Aug 3, 2021 at 17:02

Primordial have 15 segments, each with 2 paired limbs:

  • 5 arm segments ( 5/15 fire )
  • 5 wing segments ( 5/15 air )
  • 4 leg segments ( 4/15 earth )
  • 1 fin segment ( 1/15 water )

Arms and wings are not questionable here: they must be equal ("like fire and air equally"), and if there were less arms ( say 4 arm + 1 leg segments at front ), then in order to be just 4 wing segments we would need fins to cross to middle 5 segments - which would mean more fin segments (6) than wing/arm segments (4), impossible due to "like fire/air, dislike water" ( since like/dislike is related to number of corresponding limbs )

Legs and fins are less clear. But based on "a fin with 3 limbs behind", it can be assumed that those behind are not fins ( or it would be 2 fins with 2 limbs behind...). Further, it can be assumed that '3 limbs behind' are those seen on one side of primordial ( so 1 fin segment and 3 non-fin segments), since if limbs on other side are also seen/counted, there must have been at least one more fin. Those non-fin segments can only be legs, since beside fins only legs are allowed in last third ( last 5 segments).


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