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 Polyomino Puzzle (Posted on 2005-11-22)
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: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 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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