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Polyomino Puzzle (Posted on 2005-11-22) Difficulty: 3 of 5
The squares of the six polyominoes depicted below are either filled or empty. What logic was used to determine whether a square filled?
+--+--+--+--+--+              +--+--+
|##|  |##|  |##|              |##|##|
+--+--+--+--+--+  +--+--+     +--+--+
|  |  |  |  |     |##|##|     |##|##|
+--+--+--+--+  +--+--+--+--+  +--+--+
   |##|  |##|  |##|  |  |##|  |  |  |
   +--+--+--+  +--+--+--+--+  +--+--+
      |  |        |##|  |##|     |##|
      +--+        +--+--+--+--+  +--+
                     |##|  |##|
            +--+--+  +--+--+--+
            |  |##|     |##|
+--+--+  +--+--+--+--+  +--+
|##|##|  |##|  |  |  |
+--+--+  +--+--+--+--+     +--+
|##|##|        |##|##|     |##|
+--+--+--+--+  +--+--+  +--+--+--+
   |  |  |  |  |##|##|  |  |  |  |
   +--+--+--+  +--+--+  +--+--+--+
   |##|  |  |           |##|  |##|
   +--+--+--+           +--+--+--+

See The Solution Submitted by Brian Smith    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 20 of 21 |

I wonder, had anyone noticed that all the polyominoes have 1 mod 3 squares?

+--+--+--+--+--+--+ 
|##|  |##|##|  |##|   
+--+--+--+--+--+--+ 
   |  |##|##|  |
   +--+--+--+--+--+
      |  |  |  |##|
      +--+--+--+--+ 
         |##|  |   
         +--+--+

It was Brian's hint that helped a lot.  I tried making the polyominoes with the L-triominoes, but I couldn't because one square was left over.  Eventually, I figured out that the square left over was always filled.  That appears to be the rule.


  Posted by Tristan on 2006-01-29 23:38:55
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