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Spirit Web:
Can you figure out the interconnected web of affections among these characters using the provided clues?

Basic Rules:
1: There are exactly three existing relationships.
2: No character in a relationship is pursuing anyone.
3: Except as noted, all single characters are pursuing exactly 1 character.
4: There are no outside characters involved.

Characters and Clues:
Alloy (straight male): Pursued by exactly one character.
Aqua (straight female): Pursued by Fate; not pursued by anyone else.
Arc (gay male): Only character after Terra; not pursued by Emote.
Areo (straight male): Is being pursued by Frost, who is in turn pursued by Tick.
Emote (straight female): Pursuing someone no one else pursues; no one pursues Emote.
Fate (lesbian female): Pursuing two characters, one of whom pursues Alloy.
Force (bisexual female): In a relationship; no one is after her partner.
Frost (straight female): Pursued by two guys, neither of whom pursue Ivy.
Ivy (lesbian female): Pursued by two guys; pursuing one girl, who in turn pursues Fate.
Lum (straight female): Pursuing only one guy; pursued only by that guy.
Nick (straight male): In a relationship, not with Force or Volt; not pursued by anyone.
Null (straight male): Pursuing the same character as Ivy.
Psych (straight male): Not pursued by anyone.
Pyro (straight male): Pursuing two girls; pursued by two girls.
Shade (bisexual female): Single and pursued by two characters of differing genders.
Terra (bisexual male): Pursuing the same girl as Alloy.
Tick (straight male): Not pursued by anyone.
Tone (straight female): Pursuing two characters, one of whom pursues Ivy.
Volt (straight female): In a relationship; someone is after her boyfriend.

Character List:
Male: Alloy, Arc, Areo, Nick, Null, Psych, Pyro, Terra, Tick.
Female: Aqua, Emote, Fate, Force, Frost, Ivy, Lum, Shade, Tone, Volt.

Now, I am worried about two things:
1: Is the puzzle solvable with just these clues?
2: If so, are any of the clues unnecessary?

I'm fairly confident the puzzle is solvable, but I'm not quite sure.

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  • 1
    $\begingroup$ Welcome to Puzzling :)! $\endgroup$ – IAmInPLS Sep 1 '16 at 6:11
  • $\begingroup$ Not making the directed graph as this puzzle already gave me a headache :P $\endgroup$ – ABcDexter Sep 1 '16 at 7:25
  • $\begingroup$ "Lum (straight female): Pursuing only by one guy; pursued only by that guy." I don't understand "Pursuing only by one guy". Is it "pursuing only one guy" or "is being pursued by only one guy". $\endgroup$ – Marius Sep 1 '16 at 7:58
  • $\begingroup$ @Marius Both, she is pursuing 1 guy and being pursued by that same guy. $\endgroup$ – qwertyu63 Sep 1 '16 at 12:02
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I think I have it - I've come to no contradictions I can see, but a few people are left un-pursued. You didn't explicitly say that everyone was pursued by someone unless stated otherwise, so I assume it's OK to find people who aren't pursued.

Step 1:

Only Areo, Nick and Psych among the males are not known to pursue someone. Nick is in a relationship with someone who is not Force or Volt. Force’s partner must be male since the L/B females are all either pursuing someone else or being pursued by someone else, and “No one is after Force’s partner”. Likewise, Areo is discounted because someone is after him - so Force is partnered with Psych.

Step 2:

Volt is in a relationship (not with Nick). Someone is after her boyfriend. The only male not pursuing anyone and not in another relationship is Areo. He must be Volt’s boyfriend.

Step 3:

Emote is pursuing someone no one else pursues. This rules out Nick, Psych, and Tick (pursued by no one), Areo, Terra (pursued by others), and Pyro (known to be pursued by 2 girls). Alloy is pursued by someone Fate pursues; but Emote is pursued by no one, so she can’t be that person. She doesn’t pursue Arc per Arc's clue. This leaves Null.

Step 4:

The only female not pursuing anyone yet, in a relationship already, or explicitly stated as single is Aqua. She must be the female in relationship with Nick.

Step 5:

If Alloy and Terra are the two males after Ivy, only 1 person is after Terra, so Terra isn’t the one of Ivy’s pursuers who is pursued by Tone - that must be Alloy. Therefore Fate pursues Tone.

Step 6:

Null pursues someone who pursues Fate - that someone must be a L/B female. Of those: Fate won’t pursue herself; Force is in a relationship; Ivy is already pursued by two; so Null must be one of the two pursuing Shade. Ivy is then the other one pursuing Shade, by Null's clue.

Step 7:

All other males are pursuing only one person or in a relationship - so Lum must be pursuing and be pursued by Pyro.

Step 8:

Frost is being pursued by two people; Pyro is the only one left who could be her second pursuer. Pyro is being pursued by two females; Tone is the only one left who could be his second pursuer.

Answer:

Alloy: Pursues Ivy, Pursued by Tone
Arc: Pursues Terra, Pursued by no one
Areo: In a relationship with Volt, Pursued by Frost
Nick: In a relationship with Aqua, Pursued by no one
Null: Pursues Shade, Pursued by Emote
Psych: In a relationship with Force, Pursued by no one
Pyro: Pursues Frost and Lum, Pursued by Tone and Lum
Terra: Pursues Ivy, Pursued by Arc
Tick: Pursues Frost, Pursued by no one
Aqua: In a relationship with Nick, Pursued by Fate
Emote: Pursues Null, Pursued by no one
Fate: Pursues Aqua and Tone, Pursued by Shade
Force: In a relationship with Psych, Pursued by no one
Frost: Pursues Areo, Pursued by Tick and Pyro
Ivy: Pursues Shade, Pursued by Alloy and Terra
Lum: Pursues Pyro, Pursued by Pyro
Shade: Pursues Fate, Pursued by Ivy and Null
Tone: Pursues Alloy and Pyro, Pursued by no one
Volt: In a relationship with Areo, Pursued by no one

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  • $\begingroup$ You got the lot. That is the correct answer. $\endgroup$ – qwertyu63 Sep 2 '16 at 3:10

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