1.) Getting the first clue is probably the hardest in the whole puzzle. First of all, Scorpio tells you that each row and column has exactly one A or C sign. This is because there are 4 A/C signs (Aquarius, Cancer, Capricorn, Aries) and because there are 4 rows and columns. Thus Scorpio tells you that no A or C can be in A1, B1, C1, D2, D3, or D4. Aquarius tells you that Cancer is not adjacent to any sign that is not six letters. So Cancer cannot be, in addition to the above, A3, B2, B3, or C2. In other words, what’s left for Cancer is A4, C3, and C4. Cancer must be adjacent to at least three unknown cells because Aquarius tells you it is adjacent to Gemini, Taurus, and Pisces. Therefore Cancer cannot be in A4, which is only adjacent to two unknown cells. Aquarius also tells you that Cancer cannot be adjacent to 8 total cells, because it is only adjacent to three signs, and there are only 4 empty cells. This rules out the middle 4 boxes, including C3. So Cancer must be in C4.
2.) Cancer tells you that A4 is an animal. A4 is not adjacent to Cancer, so A4 cannot be Taurus or Pisces. A4 cannot be Aries either, because Row 4 already has an A/C sign in Cancer. Therefore A4 is Leo.
3.) You can now determine where the other A/C signs (Capricorn and Aries) are. If the A/C in Column B is in B3, then either Row 2 or Column A would not have an A/C. Remember that the implication of Scorpio is that that each row and column has exactly one A or C sign. So the remaining A/C signs must go in B2 and A3. If A3 is Capricorn, then B2 or B3 must be Libra. Libra cannot be in B3 according to Aquarius because it does not have six letters, but is adjacent to Cancer. Libra cannot be in B2 because it was determined that B2 and A3 are Capricorn and Aries. So if Capricorn were in A3, it would not be adjacent to Libra, as Leo says it is. therefore A3 is Aries and B2 is Capricorn.
4.) According to Capricorn, A1 and D3 have no sign.
5.) Aquarius tells you that two of B3, C3, and D4 are animals (Pisces and Taurus). Therefore C1 and D1 are clearly not adjacent to any animal sign. Thus, according to Aries, D2 is adjacent to at least one animal. A1 says that D4 is an animal, so in order for D2 to be adjacent to an animal sign, C3 must be an animal. This means that the six-letter sign in B3 is Gemini.
6.) According to Gemini, one sign is adjacent to Aries, Libra, and Virgo. Only Gemini and Capricorn are adjacent to Aries and two unknown cells, but we know that C3 is Taurus or Cancer, so Gemini can only be adjacent to two of the three 5-letter signs. Therefore Capricorn is adjacent to all three 5-letter signs. C3 is not one of them (Taurus or Pisces) and D3 says that C1 or C2 is no sign. So Virgo or Libra is in B1 and the other one and no sign are in C1 and C2. This means that D2 must be Sagittarius.
7.) The only way for Virgo not to be within two “moves” of Pisces, as Sagittarius says, is for Pisces to be in D4. Incidentally, Virgo cannot be in C2.
8.) With Pisces in D4, Taurus must be in C3.
9.) Taurus says that one of the middle 4 cells (Capricorn, Gemini, C2, Taurus) must be adjacent to seven signs (and one no sign). It’s clearly not Taurus because Taurus is already adjacent to two no signs. D3 says that Capricorn will also be adjacent to two no signs. If C2 is adjacent to seven signs, then C2 has to be no sign. Taurus says that it must be a sign that is surrounded by seven other signs. Therefore it must be Gemini. So C2 cannot be no sign; no sign must go in C1.
10.) According to Sagittarius, Virgo cannot be in C2 or it would be too close to Pisces. Therefore Virgo is B1 and Libra is C2.