War Game

"The difference between winning and losing in war," Jack was fond of saying, "hinges on decisive tactics and clever deployment of forces." This was demonstrated in the historical record of his most recent head-to-head confrontation:

  1. The final layout featured at least one winning formation of each of the 5 types (Wedge, Phalanx, Battalion Order, Skirmish Line, and Host), and at least one losing formation of 4 out of the 5 types.
  2. Neither player played a card of the same value or color as his opponent on the same flag. Neither player played a card of the same color to two of his own adjacent hands.
  3. One particular Troop value was never played at all. One particular Troop color was played fewer times than any other.
  4. One of the players could have removed any 20 active (that is, not unplayed or discarded) Troop cards on his side of the final layout and had the remaining active Troop card values on his side of the final layout sum to a positive, even number.
  5. The final layout contained more blue cards than violet cards.
  6. The green, blue, and violet Light Cavalry Phalanx in Column 1 was one of three Phalanxes in the final layout, and it faced a formation higher than a Skirmish Line.
  7. The final layout featured more than one doubleton. All incomplete hands (singletons or doubletons) at the end were either (a) a singleton orange card or (b) a non-orange Skirmisher paired with an orange non-Skirmisher. The orange Javalineer remained a singleton, and it did not lose to a Battalion Order.
  8. Each player could have played a Troop card from his hand during each of his turns, though sometimes the players chose to play a Tactics card instead. South started the game, and at some point played the only Tactics card he held all game to discard North's orange Hypaspist from play. At some point, North played the Tactics card "Fog" to Column 3 and immediately claimed that flag with a hand summing to more than 19; if North had not played "Fog" on that turn, South could have claimed that flag on his own next turn by playing a yellow card from his hand. After North played "Fog," South played no yellow cards for the rest of the game. At some point, North also played the Tactics card "Scout."
  9. The highest-ranking formation in the final layout was in Column 2.
  10. At least one Troop in North's Column 3 hand had the same value as at least one Troop in North's Column 4 hand.
  11. In the final layout, Column 5 contained 2 cards that summed to exactly 16, and Column 7 did as well, but no other column did.
  12. The first-played card in the North Column 9 formation had the same value as the first-played card in the North Column 3 formation. The second-played card in the North Column 9 formation had the same value as the second-played card in the North Column 3 formation. The third-played card in the North Column 9 formation was green, and differed by 2 from the value of the third-played card in the North Column 3 formation.
  13. Column 4 in the final layout contained cards of all 6 colors and at most 3 different values, and its cards summed to exactly 25. The first Troop played to Column 4 was green, and all Troops played to Column 4 thereafter were of a value higher than that first card.
  14. At the end, each player had at least one active card played to each flag. Throughout the contest, whenever a player could claim a flag at the end of his turn, he did. The winning player claimed his fifth flag immediately upon playing an Elephant.
  15. The red Javalineer and yellow Phalangist were part of a winning Battalion Order and losing Battalion Order (not necessarily in that order) that had different sums.
  16. North did not have a losing Host.
  17. At the end, North had a Battalion Order the sum of which differed by exactly 2 from the sum of a Battalion Order played by South.
  18. The sum of all cards appearing in single-colored hands (whether or not complete) in the final layout was not evenly divisible by 10.
  19. The unplayed Troop cards summed to exactly 81.