Musical Chairs Cipher: Double Trouble

Question

This question is a continuation of the first question: Musical Chairs Cipher.

The basic rules:

Six children -- Alice, Ben, Carl, Denise, Eddie, and Flo -- are playing a game of musical chairs in class. On each of the five chairs is written a seven letter word.

The children start out in alphabetical order, and maintain that same order through the whole game. At the end of each round, each person sits in a chair, except for one, who is out.

Then, each of the sitting children scribbles out the word on their chair, in its place writing the same word under a vigenere cipher, using their name as the key.

One chair is then removed before resuming the game, which continues until there is only one person left. When removed, the word written on the chair is no longer changed. The final chair's word is still changed by the winner.

While Alice, Ben, Carl, Denise, Eddie, and Flo are playing their musical chairs games, there is another group that is playing the same game: Andy, Violet, Wendy, Xavier, Yvette, and Zack.

For a while, the two groups are able to play separately without issues, but then the second group gets upset that the first group always gets the best words, and the first group accuses them of the same.

The teacher thinks for a few moments, then comes up with a game that will allow both teams to get their way, without lengthening each round by too much.

She tells each team that they will be swapping between their sets of chairs each round. Team one will start on set one, then set two the next round, and going back to set one the third round. Each round, one child will be eliminated from each team and one chair will be removed from each set, as normal. When moving between the sets of chairs, the children will remain in alphabetical order. The two teams will never be mixed together; they will stay separate the whole game, and the game will end with two winners.

If the game begins with the words:

CHICKEN
ROOSTER
SPARROW
TURKEYS
OSTRICH

and

VULTURE
ORIOLES
SEAGULL
PELICAN
BLUEJAY

And ends with:

DLVDORO
TWJZBEO
QBBKNLU
VBYGIYQ
LJWFNDO

and

TPPMNVC
NMFCFIJ
MBUVJOH
LTGNEWC
WXHJXXI

What order did the children get out from each team, and who are the two winners?

Answer 1

Order of Elimination:

Flo, Denise, Alice, Eddie, Carl, *Ben
Andy, Xavier, Wendy, Yvette, Zack, *Violet
*Winners

To start off we can:

Find the positional difference for each word between where it started off and the final encryption giving us the cumulative "key" that enciphers each word. Since the vigenere cipher is transitive, we can then look for the combination of children's names that sum up to that cumulative key.
For the first group we find:
chicken rooster sparrow turkeys ostrich 1 2 24 2 23 4 8 12 7 17 13 21 1 7 3 1 7 19 22 14 4 8 22 4 5 13 0 23 0 1 1 23 24 24 7
vulture orioles seagull pelican bluejay 24 25 20 22 21 21 21 23 15 12 4 23 20 21 13 19 14 15 5 5 19 20 15 2 14 4 4 3 22 23 24 17 22 15 10

In order to start idetifying where children sat we no that:

Since one chair is removed in each round, we should find one chair in each group with a key equal to the name of a child in the group that sat on it first, one chair in each group equal to the sum of a child from its first group and its second group, etc. The values for each child's name (repeated to length 7 to match the word) are:
alice ben carl denise eddie flo 0 1 2 3 4 5 11 4 0 4 3 11 8 13 17 13 3 14 2 1 11 8 8 5 4 4 2 18 4 11 0 13 0 4 4 14 11 1 17 3 3 5
andy violet wendy xavier yvette zack 0 21 22 23 24 25 13 8 4 0 21 0 3 14 13 21 4 2 24 11 3 8 19 10 0 4 24 4 19 25 13 19 22 17 4 0 3 21 4 23 24 2
We note that BEN as a key matches the value for CHICKEN and YVETTE matches for VULTURE meaning that those children sat in those chairs in round one after which those two chairs were eliminated.

This means after round 1 the seating arrangement was:

chicken rooster sparrow turkeys ostrich Alice X X X X ? Ben @ X X X X Carl X ? X X X Denise X ? ? X X Eddie X X ? ? X Flo X X X ? ?
vulture orioles seagull pelican bluejay Andy X ? ? X X Violet X X ? ? X Wendy X X X ? ? Xavier X X X X ? Yvette @ X X X X Zack X ? X X X
With @ indicating the child definitely sat there, ? indicating they might have sat there, and X indicating they did not sit there.

Now for round two:

We know two possible children that could have sat in each chair for round 1, plus any of the six children from the other group that could have sat in it for round 2, giving us 12 possible combinations to try to match the key for one of the chairs that was removed in round 2. We find that DENISE + VIOLET matches the key for SPARROW and WENDY + ALICE matches the key for PELICAN. Because of this we know that Denise, Wendy, Violet, and Alice all survived round 1. In order for there to be one chair between Ben and Denise, Carl also must as survived and similarly for Xavier. This means the seating for round 1 was:
chicken rooster sparrow turkeys ostrich Alice X X X X @ Ben @ X X X X Carl X @ X X X Denise X X @ X X Eddie X X X ? X Flo X X X ? X
vulture orioles seagull pelican bluejay Andy X ? X X X Violet X X @ X X Wendy X X X @ X Xavier X X X X @ Yvette @ X X X X Zack X ? X X X
Meaning in round 1 we now know that either Eddie or Flo from group 1 and Andy or Zack from group 2 was eliminated. The possible sequence for each chair after the first two rounds now becomes:
CHICKEN: BEN, removed
ROOSTER: CARL, [YVETTE, ZACK/ANDY]
SPARROW: DENISE, VIOLET, removed
TURKEYS: [EDDIE/FLO], [WENDY, XAVIER]
OSTRICH: ALICE, [XAVIER, YVETTE]

VULTURE: YVETTE, removed
ORIOLES: [ANDY/ZACK], [CARL, DENISE]
SEAGULL: VIOLET, [DENISE, EDDIE/FLO]
PELICAN: WENDY, ALICE, removed
BLUEJAY: XAVIER, [BEN, CARL]

Now in round 3 we are down to three total chairs:

We can apply a similar logic to determine which chair was eliminated in this round and which children sat in it. Each chair now has between 2 and 4 possible combinations of previous sitters and still all 6 children as candidates for this round. We find that the key for TURKEYS matches EDDIE + WENDY + CARL and ORIOLES matches ZACK + CARL + YVETTE. Since Eddie was around in the third round and Zack had a seat in the first round, that means Flo and Andy must have been eliminated in the first round. Since we know Yvette makes it to the third round either Zack or Xavier must be eliminated in the second round. Since there is one chair between Alice and Carl in the second round, Ben must also have a seat so either Denise or Eddie gets eliminated in the second round. Our new order for each chair looks like:
CHICKEN: BEN, removed
ROOSTER: CARL, [YVETTE, ZACK], [ALICE, BEN]
SPARROW: DENISE, VIOLET, removed
TURKEYS: EDDIE, WENDY, CARL, removed
OSTRICH: ALICE, [XAVIER, YVETTE], [DENISE/EDDIE, ALICE]

VULTURE: YVETTE, removed
ORIOLES: ZACK, CARL, YVETTE, removed
SEAGULL: VIOLET, [DENISE/EDDIE], [ZACK, VIOLET, WENDY]
PELICAN: WENDY, ALICE, removed
BLUEJAY: XAVIER, BEN, [VIOLET, WENDY, XAVIER]

Round 4, 2 chairs left:

Same process to identify the removed chair. This time we get OSTRICH as ALICE + YVETTE + EDDIE + VIOLET and BLUEJAY as XAVIER + BEN + VIOLET + CARL. Since Violet was in BLUEJAY in round 3, and Yvette was in ORIOLES, Zack must have been in SEAGULL, meaning Xavier was eliminated in round 2. There are no chairs between Violet and Yvette on the other side, so Wendy must have been eliminated in round 3. Since Eddie is in OSTRICH in round 3, Denise must have been eliminated in round 2. This leaves Alice or Ben eliminated in round 3. CHICKEN: BEN, removed
ROOSTER: CARL, ZACK, [ALICE/BEN], [YVETTE/ZACK]
SPARROW: DENISE, VIOLET, removed
TURKEYS: EDDIE, WENDY, CARL, removed
OSTRICH: ALICE, YVETTE, EDDIE, VIOLET, removed

VULTURE: YVETTE, removed
ORIOLES: ZACK, CARL, YVETTE, removed
SEAGULL: VIOLET, EDDIE, ZACK, [ALICE/BEN]
PELICAN: WENDY, ALICE, removed
BLUEJAY: XAVIER, BEN, VIOLET, CARL, removed

Final Round:

Same process, we get ROOSTER as CARL + ZACK + BEN + ZACK + BEN and SEAGULL as VIOLET + EDDIE + ZACK + BEN + VIOLET. This means Alice was eliminated in round 3, in round 4 Yvette and Eddie, in round 5 Carl and Zack, with Ben and Violet as our winners. CHICKEN: BEN, removed
ROOSTER: CARL, ZACK, BEN, ZACK, BEN winner
SPARROW: DENISE, VIOLET, removed
TURKEYS: EDDIE, WENDY, CARL, removed
OSTRICH: ALICE, YVETTE, EDDIE, VIOLET, removed

VULTURE: YVETTE, removed
ORIOLES: ZACK, CARL, YVETTE, removed
SEAGULL: VIOLET, EDDIE, ZACK, BEN, VIOLET winner
PELICAN: WENDY, ALICE, removed
BLUEJAY: XAVIER, BEN, VIOLET, CARL, removed