Stacks: b1 w2 r3 g4 y5
Alice: b2 w3 r4 g5
Bobby: y1 y1 w1 b5
Carol: g1 g1 b2 r4
David: r1 w3 w4 w5
Wins: 4
Deck: r5 .. w4 b3 b4 .. kt kt
Line: g5 .. r4 w3 r5 .. b2 b3 b4 b5 w4 w5
Plan: F  I  V  E  S  W  I  N  T  H  I  S
Display: Fives win this

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[F] Turn  1 ..... Alice plays [W] green 5 and draws [U] red 5
[I] Turn  2 ..... Bobby stalls by spending a clue
[V] Turn  3 ..... Carol plays [P] red 4 and draws [T] white 4
[E] Turn  4 ..... David plays [O] white 3 and draws [N] blue 3
[S] Turn  5 ..... Alice plays [U] red 5 and draws [S] blue 4
[W] Turn  6 ..... Bobby stalls by spending a clue
[I] Turn  7 ..... Carol plays [I] blue 2 and draws any card
[N] Turn  8 ..... David plays [N] blue 3 and draws any card
[T] Turn  9 ..... Alice plays [S] blue 4 on their last turn
[H] Turn 10 ..... Bobby plays [X] blue 5 on their last turn
[I] Turn 11 ..... Carol plays [T] white 4 on their last turn
[S] Turn 12 ..... David plays [Y] white 5 on their last turn

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PROOF OF UNIQUENESS

The initial pace is 0.
Therefore, no discards are permitted and every player
must play in the final round.

Bobby starts with no playable cards,
so until Bobby has a playable card, he must be given clues to spend.

Thus, Alice must play g5 to begin.
Bobby then spends a clue.

Looking ahead, the only way to complete a 5 before Bobby's next turn
is for r5 to be played since no other 5 is close enough.
So Alice must have drawn r5,
and Carol must play r4 into it.
David plays his only option w3,
and thus Alice plays r5.
Bobby spends a clue.

At this point, there are two cards remaining in the deck, and zero clues.
As no player may discard, this means Bobby gets at most one more turn.
Thus, the blue 5 must be playable by Bobby's next turn.
Hence Carol, David, Alice must play b2, b3, b4 in that order,
so that Bobby can play b5.

At this point, only two turns remain, so Carol and David must play w4 and w5.

Examining the deck ordering, we see there are two unused cards.
One of them must be David's final draw.
The other is one of Carol's draws --- she must draw w4,
but the w4 and her unused draw can come in either order.
Of course, the two unused cards are interchangable.
This means there are 2 * 2 = 4 orderings of the deck
which lead to victory,
according to which of the two trash card Carol draws,
and which position it is in.