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Monday, January 28, 2013

Dominoes rules

A set of dominoes has been laid out in a grid and the edges erased.  You must determine where the edges go.  The solution is unique.

Here is a sample and its solution:




Most puzzles will include a set of dominoes to the side for checking off used dominoes.  Unfortunately, I have not found a completely suitable domino applet yet.  www.puzzlepicnic.com has one, but it doesn't support the double nine dominos that I used for the first puzzle.

Edit: I know it has been years since I have posted anything on this site, but I decided to dust it off today and look at it.  When I did that, I noticed that there is a bit of a flaw in my sample puzzle, depending on your definition of the rules of a unique solution.  According to my definition, it is a flaw.  

The solution is not unique, in that everything can be solved uniquely up until the last four dominoes in the upper right corner.  The way I have the solution posted above is not a unique solution, as the 3/2, 3/1, and 2/1 dominoe can be moved around to provide another solution. In my definition of unique, this is not allowed and the mistake was mine as I did not intend the puzzle to work out this way.  However, the 1/1 domino can also be positioned vertically instead of horizontally, which leads to the following solution:
Working this way, we can see that this does force a unique solution.  So here's the rub: Some puzzlers consider the unique solution to be a condition that must be followed during the solving process, rather than a constraint on the solution, if that makes any sense.  The logic proceeds like this:  I have reached a point where I have to make a guess.  If I choose guess number one, the logic chain proceeding from that guess allows multiple solutions.  If I choose guess number two, the same thing could happen again.  Repeat until you get to the final guess.  This guess does lead to a unique solution.  Therefore, that must be the correct guess.  I don't really like this kind of puzzle.  For some reason, it just seems like the puzzle is cheating.  I like my puzzles to have one solution, and one solution only.  In fact, it wouldn't even be appropriate to say that my puzzle has a unique solution, because unique implies that one solution stands out different from the rest.  I would define the solution to my puzzles to be the solution.  I will leave this sample puzzle in the blog as it is for demonstration, but if you ever find one of my puzzles with a non-unique solution, please bring it to my attention, because that would've been an error in the design process.

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