Stacks: r2 b3 g4 y5 Alice: b1 b1 g5 b5 Bobby: r1 r4 w4 w4 Carol: y1 y1 w3 w3 David: g1 g1 w2 w2 Wins: 12 Deck: r3 .. w1 .. r5 kt w5 b4 kt .. kt Line: g5 .. dc .. r3 r4 w1 w2 r5 .. w3 b4 b5 w4 w5 Plan: F I R E E P I C B L O S S O M Display: Fire epic blossom ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ [F] Turn 1 ..... Alice plays [W] green 5 and draws [K] red 3 [I] Turn 2 ..... Bobby stalls by spending a clue [R] Turn 3 ..... Carol discards a stale card and draws [E] white 1 [E] Turn 4 ..... David stalls by spending a clue [E] Turn 5 ..... Alice plays [K] red 3 and draws [U] red 5 [P] Turn 6 ..... Bobby plays [P] red 4 and draws any card [I] Turn 7 ..... Carol plays [E] white 1 and draws [Y] white 5 [C] Turn 8 ..... David plays [J] white 2 and draws [S] blue 4 [B] Turn 9 ..... Alice plays [U] red 5 and draws any card [L] Turn 10 ..... Bobby stalls by spending a clue [O] Turn 11 ..... Carol plays [O] white 3 and draws any card [S] Turn 12 ..... David plays [S] blue 4 on their last turn [S] Turn 13 ..... Alice plays [X] blue 5 on their last turn [O] Turn 14 ..... Bobby plays [T] white 4 on their last turn [M] Turn 15 ..... Carol plays [Y] white 5 on their last turn ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ PROOF OF UNIQUENESS In this scenario, the w2, w3, w4 are all present, but unluckily they are in reverse order. Moreover, w1 is missing. The starting pace is +1. However, only Alice has a play on the first turn, so one of the other three players is going to have to discard on the first round. We claim that the number of turns that can occur is at most 16. There are four turns in the final round, and up to eight plays/discards. Also, one can get at most four clues before the final round: three from 5's and one from discarding. Thus, the upper bound on the number of turns is 8+4+3+1 = 16. This already implies that w2 must play on turn 8, w3 must play on turn 11, and w4 must play on turn 14, in order to finish in time. In order to not lose the first round, the team needs to orchestrate one discard and two clues. So Alice must play g5 to begin. We claim Bobby must clue on his first turn. If Bobby discards, pace drops to 0, and Carol and David must clue. However, this will leave Carol with no plays on turn 7, contradiction. This forces Carol to discard. At this point, Bobby needs a play on turn 6. The only way this can happen is if Alice draws r3. But we already knew that w2 plays on turn 8, therefore Carol must draw w1 right now. David then spends the last clue. The next four plays r3, r4, w1, w2 are forced as these are the only playable cards on each of these turns. At this point, Alice must play r5 on her turn (her drawn card), because otherwise Bobby triggers the last round and there is no way to have w5 played in time. So Alice should play r5 and let Bobby hint so that Carol can play w3 and begin the final round. With four turns left, the plays must be b4, b5, w4, w5, since Alice holds the only b5. Looking at the deck order, there are 3 unused cards which can be arranged in any of 3!=6 ways.