CiSRA Puzzle Competition 2010 - Solutions
The first step is to identify all the dominoes. There are 28 dominoes, which is the correct number for a standard set of double-6 dominoes. If you assume this, then you can identify all of the dominoes unambiguously. Here's a photo of the dominoes after they've been toppled, so you can more easily see their identifications.
The next thing to notice is the positions of the blank half-tiles. Here you can see that every branch in the toppling chain occurs at a blank. (There's also one blank that doesn't produce a branching, on the blank-4 domino at upper left.)
This suggests grouping the domino halves by sectioning them off in between the blanks. Here we've circled the groupings.
Count the total number of pips in each grouping. If you convert these to letters (using 1=A, 2=B, etc.), you get the following result.
Reading up from the beginning of the toppling chain we can see the word "END", followed by the double-blank domino, which splits the toppling chain into two large branches. The leftmost branch spells "TILE". The rightmost branch is a little messier, but a depth-first traversal spells "LETTERS". This gives the message "END TILE LETTERS". (This is not strictly a depth-first traversal of the entire domino tree; the double-blank acts as a word separator, extending the idea that blank half-dominoes act as letter separators.)
The message means that you need to examine only the end tiles of the toppling chain. That means dominoes that don't hit any other dominoes when they fall over. The 2-2 domino at the bottom doesn't count, since it's at the beginning. If we look at the pip count of the end tiles alone, we get the following.
These letters have only one anagram into an English word, the solution: EDIFICE.
Puzzle design notes: During testing, some testers argued that the beginning domino of the toppling chain could also be considered an "end" tile. Its letter value is a "D". So we also accepted the word EDIFICED as a possible solution (though no teams entered it as an answer).