Introducing the Snail puzzle<\/h3>\n
Two months ago, I decided I wanted to tackle the Snail puzzle (which I found in 100 Logic Games<\/a>).<\/p>\n The gameboard is a grid of squares, which are marked out as a spiral. Each cell can marked as “empty” with a dot, or marked as having a 1, 2, or 3 in it. Some are filled in as initial clues.<\/p>\n The rules are are: <\/p>\n I implemented this a few months ago, so I am a little vague about my motivations.<\/p>\n I recall I had some ideas about adopting a different approach than normal. I was considering trying a more brute-force method, because I thought I could model the problem in a way that the number of combinations to try was very small (i.e. in the millions).<\/p>\n When I did the maths, it didn’t scale well. The 5×5 puzzle above could be solved quickly, but an 11×11 was infeasible.<\/p>\n So, I used my tried-and-true technique of the framework I wrote all those years ago.<\/p>\n I had another hypothesis that a couple of simple logical inference rules might be sufficient to solve the puzzles, if I modelled it right.<\/p>\n In particular, I didn’t model each cell as having one of four values, but as having one of six values: 1, 2, 3, \u00e2\u2014\u008f1, \u00e2\u2014\u008f2, \u00e2\u2014\u008f3.<\/p>\n The three dotted values were displayed as a single dot (i.e. an empty cell), but behind the scenes the rules were more complex. A \u00e2\u2014\u008f1 cell could only be followed by a 1 cell or another \u00e2\u2014\u008f1 cell. A 1 cell could only be followed by a 2 cell, or a \u00e2\u2014\u008f2 cell. This allowed information about what the last cell was to be carried around the corners.<\/p>\n It seemed to work. A implemented those constraints, plus the typical exactly-one-number-per-row exclusion rules – i.e. if there is a 3 in this row, no other cell in this row can be a 3. If no other cell *might* be a 3 in this row, this cell must be a three.<\/p>\n Those rules were sufficient to solve most of the puzzles I sampled.<\/p>\n![\"A](\"http:\/\/www.somethinkodd.com\/oddthinking\/wp-content\/uploads\/2018\/06\/Game1_unsolved-279x300.png\")
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Solving the Snail<\/h3>\n
![\"\"](\"http:\/\/www.somethinkodd.com\/oddthinking\/wp-content\/uploads\/2018\/06\/Game1_solved-279x300.png\")
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![\"\"](\"http:\/\/www.somethinkodd.com\/oddthinking\/wp-content\/uploads\/2018\/06\/Game3_partiallysolved-290x300.png\")
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