A cubic piece of cheese has been subdivided into 27 subcubes (so that it looks like a Rubik's Cube). A mouse starts to eat a corner subcube. After eating any given subcube it goes on to another adjacent subcube. Is it possible for the mouse to eat all 27 subcubes and finish with the center cube?

      

   No- it is not possible                    

Since each single step changes the coordinates' parity from ODD to EVEN  and vice versa ,= moving from (0,0,0) to (1,1,1) cannot be

.accomplished in 26  (or any other even number of )steps

Edited on June 13, 2013, 9:22 am

Posted by Ady TZIDON on 2013-06-12 10:08:34