I had a 6x7 chocolate bar. My kid stole a 2x3 piece from a corner. Can I divide the rest in two identical pieces, just cutting along the lines? In three identical pieces? In four?

+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+

If the obverse and reverse sides of the original chocolate bar had no differences, then one can divide the chocolate bar into either two and four identical pieces by a rotational "flip" of one of the pieces as it is a mirror image (rotationally) of the other(s), else -- by the definition of identical -- we can not divide the chocolate bar into two or four identical pieces. 

+---+---+---+---+
|   |   |   |   | 
+---+---+---+---+
|   |   |   |   | 
+---+---+---+---+
|   |   |   |   | *---+---+---+ 
+---+---+---+---+ |   |   |   |
|   |   |   | +---+---+---+---+ 
+---+---+---+ |   |   |   |   |
|   |   | +---+---+---+---+---+ 
+---+---+ |   |   |   |   |   |
|   | +---+---+---+---+---+---+ 
+---+ |   |   |   |   |   |   |
      +---+---+---+---+---+---+

+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   |   |   |   |
+---+---+---+---+
|   | +---+---+---+---+ 
+---+ |   |   |   |   | +---+---+    
      +---+---+---+---+ |   |   |   
+---+ |   |   |   |   | +---+---+   
|   | +---+---+---+---+ |   |   | 
+---+---+---+---+ |   | +---+---+ 
|   |   |   |   | +---+ |   |   | 
+---+---+---+---+   +---+---+---+
|   |   |   |   |   |   |   |   | 
+---+---+---+---+   +---+---+---+
                     

Posted by Dej Mar on 2008-02-22 09:27:01