Who is your secret santa?

Question

My first puzzle question here. I hope this meets your quality standards. :-)

First a short anecdote about the puzzle, that has no relevance if you just want to solve it: Over a number of years, I was - and still do - frequent a danish boardgame website. A lot of the users had met face to face and knew a lot of other users, and one christmas we did this secret santa thing, where each participant was assigned a target, and sent them some sort of boardgame gift. I knew my target enjoyed deduction games, so I included a puzzle I made up myself, that could help her deduce who her secret santa was. Thus the title of the puzzle.

For this puzzle, I've changed the original names of the persons, to make it easier for non-danish users to deduce which names are male or female. That and one name was "Steen" (me) which would be kind of a spoiler. ;-)

Unless you've got an eidetic memory like Sheldon Cooper, fetch pen and paper. You will need it. :) Oh, and no need for lateral thinking here. There are no "transgender santas" or something like that. The puzzle should be fairly straightforward deduction.

The puzzle:

So. You like deduction? Then I will give you some information that may tell you who I am.

Imagine nine persons sitting in a circle. All facing the centre of the circle. You don't know who is who, as they are all dressed up as santas.

They are sitting like this:

       1
  9         2
8             3
  7         4
     6   5

The santas in the circle are Anna, Susanna, Jolene, Mary, Michael, Robert, Joe, Christian and Jacob. But they are most certainly not seated in that order.

All the santas knows who is who and where they are seated.

One of them is your secret santa, and they all know who it is.

The santas will now - in turn order - show you signs with a number of statements, that may help you figure out who your secret santa is.

But it shouldn't be too easy.
Three santas will always lie.
Three santas will never lie.
And three santas may either lie or not, but will not stick to just one or the other.

Enjoy Sherlock.

First round:
Santa 1: I am female
Santa 2: Santa 1 is a male
Santa 3: Santa 1 is a female
Santa 4: Santa 1 is a female
Santa 5: Santa 1 is a male
Santa 6: Santa 1 is a female
Santa 7: Santa 1 is a female
Santa 8: Santa 1 is a male
Santa 9: Santa 1 is a female

Second round:
Santa 1: Santa 3 lies at least sometimes
Santa 2: Jacob and Mary are not seated next to each other
Santa 3: Santa 9 is a male
Santa 4: Santa 9's next statement will be a lie
Santa 5: Joe is sitting next to me
Santa 6: Both the santas sitting next to me are male
Santa 7: I don't know if I am your secret santa
Santa 8: I am your secret santa
Santa 9: The santas sitting next to me are not the same gender

Third round:
Santa 1: Santa 4 never lies
Santa 2: Santa 4 lies at least sometimes
Santa 3: Robert and Jacob are seated next to each other
Santa 4: A santa that lies sometimes, will change back and forth between the two
Santa 5: All female santas always lie
Santa 6: None of the santas seated next to me is your secret santa
Santa 7: Santa 1 lies sometimes
Santa 8: Santa 4 is either Christian or Jacob
Santa 9: If santa 3's next statement is true, santa 6's next statement will also be true

Fourth round:
Santa 1: None of the santas seated next to me is named Joe
Santa 2: Chistian is not santa 6 or 7
Santa 3: Both the santas sitting next to me are male, and one of them is Joe
Santa 4: I have one male and one female sitting next to me
Santa 5: I have males seated next to me on both sides
Santa 6: Anna is either santa 1 or 2, and Michael is sitting next to her
Santa 7: Either Mary or Jolene is the highest numbered female santa
Santa 8: Jolene is santa 6
Santa 9: Your secret santa is female

The santas will now show signs with statement that give you numbers.
None of the santas will lie anymore.
Write down the numbers in the order you get them, but only if their statement is correct.
If the statement is incorrect, you should simply skip the number.

Santa 1: Given Michael is seated next to me, my number is 9
Santa 2: Given I am seated between Anna and Jolene, my number is 3
Santa 3: Given Anna is santa 7 or 8, my number is 1, and you should reorder your numbers in descending order from 9 to 1
Santa 4: Given I am Christian, my number is 5
Santa 5: Given both the santas seated next to me are same gender, my number is 7
Santa 6: Given Jacob is sitting next to me, my number is 2
Santa 7: Given Robert and Jolene are sitting next to each other, my number is 4
Santa 8: Given all Marys statements were true, my number is 8
Santa 9: Given Christian and Jolene are seated next to each other, my number is 6 and you should reorder all your numbers in ascending order from 1 to 9

You should now have a number with an uneven amount of digits.
The middle digit is the number of your secret santa.

Answer 1

Okay, I think that your Secret Santa is

Joe (Seat 2).

From the first statement, we can deduce that

Santas 2, 5, and 8 are either always liars or always truthtellers. Santa 5 says that "All female Santas are always liars - this is impossible since there are 4 female Santas and three liars. Therefore 2, 5, and 8 are always liars. From the 3rd statement, Santa 2 says that 4 lies sometimes. This is false, so 4 always tells the truth. This is important, because it means that 4's statement that "sometimes liars" will alternate between truth and lies is true. Further, 4's second statement, that 9's second statement will be a lie, indicates that 9 is a sometimer. 7 says in their second statement that they don't know if they are your Secret Santa -- that's clearly a lie, so 7 is also a sometimer. But 7's second statement is false, so their third statement is true, so 1 is a sometimer. This means that 3, 4, and 6 are always truth tellers.

Summary of Liars/Truthtellers:

Liars: 2, 5, 8;
Truthtellers: 3, 4, 6;
Sometimers: 1, 7, 9.

We'll now start to place the characters:

1 lies in the 4th round, and so Joe is either 9 or 2. 3 says that Joe is sitting next to him, therefore Joe must be 2. 6 says that Anna is either 1 or 2, so Anna must be 1. Michael sits next to her, so Michael must be 9. Michael's second statement is a lie, so both 8 and 1 are the same gender. Anna is 1, so 8 must be female (and is the highest numbered female, too). 7 lies in the 4th round, so Mary and Jolene cannot be 8; this leaves Susanna as 8. From 3's third statement, 4 is male. From 5's fourth statement (a lie), he has different genders sitting on either side. Therefore 6 is female. She can't be Jolene because of Susanna's 4th lie, so Mary must be 6. 6 is a truth teller, so from her second statement 5 and 7 are males. We therefore have that 2 (Joe), 4, 5, 7, and 9 (Michael) are males, so by process of elimination, 3 must be female and so Jolene must be 3. Jolene says that Robert and Jacob sit next to each other, so they must be 4 and 5 in some order; 2 lies and says Jacob doesn't sit next to Mary, so Jacob must be 5 and Robert must be 4. This leaves Christian as 7.

Summary of Characters:

1: Anna (Sometimer);
2: Joe (Liar);
3: Jolene (Truthteller);
4: Robert (Truthteller);
5: Jacob (Liar);
6: Mary (Truthteller);
7: Christian (Sometimer);
8: Susanna (Liar);
9: Michael (Sometimer).

Then we have (number in brackets)

1: TRUE (9)
2: TRUE (93)
3: FALSE (93)
4: FALSE (93)
5: FALSE (93)
6: TRUE (932)
7: TRUE (9324)
8: TRUE (93248)
9: FALSE (93248)

The middle number is therefore

2

and so your Secret Santa is

Joe.