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