First, notice that the names are in alphabetical order. This should help you locate names when clues refer to it. Secondly, notice that each name has either a male symbol ♂ or a female symbol ♀. That will also help you determine who is which gender if the names seem ambiguous.
1.) Eve tells you that Cleo and her twin brother did not go. So Cleo was (A)bsent. You might argue that it doesn’t say she was “absent,” so she could still be the birthday kid, but the directions say that only one kid had a birthday. If Cleo has a twin, then it would be 2 kids’ birthday. So Cleo is (A)bsent.
2.) Adam tells you that Eli was not (A)bsent. Cleo tells you that no one who shares a diagonal with Dom is the (B)irthday kid, including Eli. Therefore Eli must have been a (G)uest.
2.) Since Cleo and Cora are the only girls in Row 2, Cleo tells you that Cora must have been a (G)uest.
3.) Cleo tells you that Bella was a (G)uest.
3.) Eli tells you that his brother is adjacent to 5 people: 4 boys whose status is unknown and 1 girl who was (A)bsent. The only people adjacent to 5 people are the ones on the outer edge, but not the corners. Eli says “brother,” so he must be male. The only boys who are adjacent to 5 people are Cain, Eli, Bud, and Auron. Of those, only Auron and Bud are adjacent to 4 boys and 1 girl. But the girl adjacent to Bud is already known to be a (G)uest. Therefore Auron is Eli’s brother, and so according to Eli, Alice was (A)bsent.
4.) Cora now tells you that Addy was a (G)uest.
5.) Bella tells you that Diane was not a (G)uest, since Addy is a (G)uest. If Dom and Diane are the same, they must both have been (A)bsent. There is only one (B)irthday kid, and Cleo tells you it’s not Dom anyway.
6.) In order for half one’s adjacents to be a whole number, that person must be adjacent to 8 people. So Cora’s crush must be Ben, Clint, Blane, Colt, or Dom. Cora also says her crush was a (G)uest, ruling out Dom. Cora also says her crush is adjacent to Bella, leaving only Ben and Clint. Ben and Colt are both adjacent to Clint, and at least one of them was (A)bsent, according to Dom. So if Blane was not a guest (alice) and Ben and Colt were not both guests, Clint can only be adjacent to 3 (G)uests. But Cora’s crush is adjacent to 4 (G)uests. Therefore Cora’s crush is Ben, and she says that he is also a (G)uest.
7.) Dom now tells you that Colt was (A)bsent.
8.) Alice says Blane was not a (G)uest. You know from Cora that Ben must be adjacent to 4 (half of 8) (G)uests. Therefore both Auron and Clint were (G)uests.
9.) Auron tells you that the (B)irthday kid is a boy. This obviously rules out (B) for all girls. So according to Bella, Emma must have been (A)bsent.
10.) Cleo now tells you that Edith must have been a (G)uest.
11.) It’s important that Edith goes through every possible scenario for Dalia. We know that it was not Dalia’s (B)irthday, because Auron said it was a boy. So Dalia was either absent or a guest. Therefore Bud was either a (G)uest or the (B)irthday kid. He was not (A)bsent. If you look at Eve’s clue and Diane’s clue, you notice that you still don’t know who Cleo’s twin brother is. He must be a boy who doesn’t have a 4-letter name. He must not be adjacent to Cleo. And he must have been (A)bsent. Nobody who is revealed fits that description. The closest is Dom, but Ben says his only sibling had a different status, but Dom and Cleo have the same status. Of those not yet revealed, Barb is a girl, Cain has 4 letters, Dalia is a girl, Earl has 4 letters, Dee is a girl, Axel has 4 letters, and Dora is a girl. Cleo’s twin must be Blane or Bud, but we established at the beginning of this step that Bud was not (A)bsent, which Cleo’s twin brother must be. Therefore Blane is Cleo’s twin brother and was (A)bsent.
12.) The diagonal Blane speaks of must be either Barb-Cleo-Diane-Emma or the main diagonal from Earl to Axel. No other diagonal could possibly contain 4 (A)bsentees. This means that Dee and/or Barb must have been (A)bsent. They cannot both have been (G)uests or no diagonal would have 4 (A)bsentees. Therefore, according to Clint, it was not Bud’s birthday. According to Edith/the beginning of step 11 above, Bud was not (A)bsent either. So Bud was a (G)uest.
13.) Because Edith goes through all of Dalia’s options, the “if”s are effectively “if and only if”s. Therefore, since Bud was a (G)uest, Dalia must have been (A)bsent.
14.) The implication of Dalia’s clue is that no row has an equal number of (G)uests and (A)bsentees. So in effect, the (B)irthday kid cannot be in a row that already contains 2 (G)uests and 2 (A)bsentees. This rules out Row 3 and Row 5. Since we know it was a boy’s (B)irthday from Auron, all that’s left is Axel. Axel is the (B)irthday kid.
15.) Now you know that the main diagonal from Earl to Axel cannot have 4 (A)bsentees. So according to Blane and step 12 above, Barb must have been (A)bsent.
16.) Barb’s clue can only be talking about Eve, and only if Dora was not a (G)uest. You know it was Axel’s (B)irthday, so Dora must have been (A)bsent.
17.) Cleo now tells you that Dee must have been a (G)uest.
18.) Dee tells you that Colt is saying “Cain,” whom she says was a (G)uest.
19.) Dee and Dora were different. Therefore, according to Bud, Cain and Earl must also have been different. Axel was the (B)irthday kid, so Earl must have been (A)bsent.