CISRA Puzzle Competition 2012 - Solutions

1A. Follow the Leader

The letters and numbers represent playing cards - there are exactly 52 boxes and each letter/number appears four times. However, the suit is only given for one of the cards: The queen of spades. The other cards still need to have their suit determined. There is also the question of how the cards are arranged in the 4×13 grid.

The card layout suggests, among other things, a trick-taking game such as Whist or Bridge - the title of the puzzle hints at this as well. The queen of spades in particular stands out as the only card with a given suit. This card is special to the game of Hearts, suggesting that might be the game being played. One of the conventions in Hearts is that the first card led is the 2 of clubs, and it can be seen that a 2 appears in the top left, potentially indicating a first lead. This suggests the club suit as the suit for the first trick.

With or without the realisation that the game is Hearts and the first suit is clubs, you can start figuring out the suits of each of the cards played. Along the way, you can make a number of discoveries. The order in which you figure these out is not set, as each of them helps to confirm the others.

• The highlighted cards are those which were off-suit; i.e., discarded because the player had no cards of the suit led. Some clues to this include the fact that every time there are two of the same value in a row one of them is highlighted (the 7s in row 7 and the Ks in row 11), and the fact that the highlights mostly appear later.
• There are two reasonable intepretations of the columns, one that they correspond to particular players, the other that they correspond to the order the cards were played in each trick. The play is more consistent with the first possibility, but more importantly knowing the highlighted cards are discards knocks out the second possibility entirely, as some highlighted cards are in the first column.
• The play is much more consistent with Hearts than other trick-taking games. The game of Hearts is notably different from most other trick-taking games in that players are not trying to win as many tricks as possible, but instead trying in general to avoid winning tricks - at least until it's clear that there are no point-cards in the trick.

Armed with that knowledge, the cards can begin to be identified. Spades are identified in the puzzle by the queen of spades (and the other tricks that fit with it). Clubs are similarly identified by the two of clubs in the first trick. However, nothing can break the symmetry between the two red suits, hearts and diamonds. Attempting to resolve the two based on the play is not compelling; the play is definitely imperfect in either case. The trick to the puzzle is to accept the ambiguity and continue working along both cases.

These are the two possible suit assignments:

The insight for the next step is that Hearts has a scoring mechanism. Figuring out the scores for the two configurations gives the following scores for each player, ordered by column:

3, 1, 18, 4 or 7, 1, 13, 5

Mapping those numbers to letters by alphabetic position gives two words: "card" and "game". Putting the two of these together yields the solution: CARDGAME.