The squares of the six polyominoes depicted below are either filled or empty. What logic was used to determine whether a square filled?

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

After much toil and hardship (and actually cutting out the polyominoes), I have reached the conclusion that the logic is of one of two possible natures.

1) Either he flipped a coin and heads meant filled in and tails meant not.

2) Or he flipped a coin and tails meant filled in and heads meant not.

My theory is that since the heads side is a bit heavier than the tails side, the coin would most likely fall heads side down, and since there are less filled in spaces than not, possibility 1 is correct.

Posted by Joe on 2005-11-26 19:52:07